Brilliant but Lazy: Luca and Paolo are actually pretty good in their respective jobs- when they fail it isn't because they're not skilled, but because fate said so. With that said, good luck seeing them working: they'd much rather spend their time in the Relax Area than doing something constructive.
Paolo: "I might be a beast but I'm a professional, for the love of..."
The Bully: Luca and Paolo are two bullies picked on by another bully (Andrea, of course).
While Paolo is implied to be a bully and a Jerk Jock even when he was in high school, Luca used to be the Butt Monkey of his class, mercilessly bullied by all his classmates.
Vittorio: "Ah, if it isn't that little comunist bastard with his tall, brainless pal!"
Geller "In the ancient region of..." following a boring story about ancient chinese populations.
Chuck Cunningham Syndrome: Several characters did just disappear without being mentioned again, most notably: Anna (one of the most prominent characters in the first two seasons), Jessica, Anselmo, psychologist Nadia along with other minor characters. But the biggest change was in the fifth season starting in 2011: Ilaria, Gaia, Giovanna, Emma, Maria Eleonora, Caterina and Carminati are all missing in the new episodes and seem to be just forgotten by the other characters.
Comes Great Insanity: De Marinis once challenged Luca to become "boss for a day", since the latter accused the former to be unfair and declared to be a way nicer boss if given the chance. By the end of that very sketch, he became so "good" at giving orders to prompt a company-scale rebellion.
Couch Gag: in the beginning, the opening for each sketch provided the series' logo, printed on a small plastic glass while it gets filled with coffee. Then, in the second season, a few variations have been made, such as both the plastic glass and the stream of coffee being misplaced, or the plastic glass being flipped over by the coffee itself. The third season upped the ante with even more absurd variations such as the plastic glass slowly lowered by chains and filled with concrete, a small scuba-diver-action-figure popping up from the plastic glass, the plastic glass being absent and the coffee flooding everything, the plastic glass glowing in the dark, a fish falling off the machine...
Geller:"Next time you'd better be more careful about when taking a vacation then; turned out we'll both be away from work within the same time range, instead of you coming back to work when I'm on holiday."
Dumb Is Good: All the stupid characters (like Patti, Silvano, Anna, Wanda, Gloria...) tend to be way too naive and innocent to be as mean and cynical as others. Patti in the later seasons is far less naive and more and more shrill and bossy.
Subverted with Paolo who is dumb and just as much of a Jerkass as his smart friend Luca.
Also subverted with Vittorio who is an insane idiot and one of the most sociopathic characters on the show.
Enemy Mine: Arch enemies Ilaria and Gaia on a few occasions teamed up against Luca and Paolo.
This is the point of the whole relationship between Luca and De Marinis. They are openly hostile to each other, the former being a "Communist" who claims the director his natural enemy because of their opposite political leanings, but actually they are always making secret agreements and plotting together against the other workers for their own personal profit (and everyone knows it, as lampshaded in season 4 episode "Il blog di Patti").
Evil Versus Evil: Luca vs. De Marinis, Luca/Paolo vs. Andrea are the most frequent.
One episode puts the two office's resident psychopaths (Andrea and Vittorio) against each other. Aside from that episode they don't have other scenes together though.
Exact Words: in one episode, Jerk Ass director De Marinis is about to install an answering machine as a replacement to textbook Sexy Secretary and resident Ms. Fanservice Giovanna, prompting Gonk, Butt Monkey and Dirty Old Woman Wanda to comfort her by saying "you're young and pretty, you won't have any problems trying to find another job"; De Marinis replies that "this is why her new job will be yours, Wanda. We need an intern". Giovanna's solution is asking resident Nerd and Playful Hacker Olmo's help in order to mess around with the answering machine, only for Casanova Wannabe Paolo finding out about it instead. Giovanna then points out she'll need the help of them both, as her "reward" can be shared. Given that A Threesome Is Hot, Olmo and Paolo eagerly team up and accept, and at the end of the episode, nobody gets fired. Cue the usage of Exact Words: Giovanna points out the two guys will get rewarded by the one who actually risked to lose her job: in other words... Wanda.
Also Paolo. In season 1, with all his flaws, he still had a common sense, he was just less book smart than Luca. In later seasons, he was really dumbed down, to the point he never gets the simplest thing and Luca has to explain anything to him multiple times. His idiocy reached its peak in season 4 though, it was a bit toned down in season 5.
Silvano was less of a wimpy doormat in the very first episodes. He was still a Butt Monkey but he was actually able to react to people and in one episode after being insulted by Luca, he loudly yells back at him. In later episodes, apart from very rare Berserk Button moments of unexpected violence, (possibly Moment Of Awesome) he was a total Extreme Doormat.
Foolish Sibling, Responsible Sibling: Paolo's sons Brad (foolish) and Jonathan (responsible). Interestingly, in the beginning they are both shown as Enfant Terrible, but at some point, to Paolo's absolute dismay, the oldest son Jonathan started reading, studying and getting good grades. Obviously Paolo is often mad at him because of it and favours little criminal Brad instead.
Friend Versus Lover: There are quite a few episodes with Paolo and Alex fighting over Luca. That inevitably ended up with Luca having a rare Pet the Dog moment trying to make happy both of them at the same time...only to discover that they actually don't care about him at all and that decided to spend time with each other instead. Leaving him alone, as usual.
Gosh Dang It to Heck!: while minor swears are allowed within the show, most of the dialogue borders on this even when characters are particularly pissed. This doesn't mean there aren't rare exceptions.
Granola Girl: Patti, Alex, Anna and Maria Eleonora all show signs of this.
I Was Quite a Fashion Victim: Season 3 includes a dozen of episodes entitled "The last century". Each of them shows the very first day at work for every employee (a long time ago) and everyone is seen with ridiculous outfits and weird hairstyles.
Jerkass: Everyone, with Luca, Paolo, De Marinis, Andrea, and Vittorio being the best examples. Also Alex who is a big Jerkass to Luca (she gets better in season 5 though) and Geller, the Magnificent Bastard.
Even the supposedly "nice" Patti is evolving into this more and more.
Karma Houdini: it doesn't matter how much of a slut Alex is, she never pays for it. Likewise, anyone who acts as the "villain" of the sketch equally never pays for it.
Definitely Andrea, annoyingly so. Every single character (including Alex, Gaia, De Marinis, even Geller) gets some humiliation or punishment in at least one episode. But there's basically no episode in which Andrea gets any sort of karmik comeuppance for being right-down sadistic and cruel.
Luca and Paolo depending on the episode, although most the time they get the karmik punishments that they deserve (usually thanks to Andrea or Geller).
Love Redeems: parodied in the episode "La Bella e la Bestia" ("The Beauty and the Beast") where Andrea, after a one-night stand with Gaia, claims to be madly in love with her and tells Luca and Paolo that he wants to be a better, nicer person just for love. Luca and Paolo obviously take advantage of the situation and start to pick on the new nice Andrea, who doesn't react violently anymore and he's basically become another Silvano. When Gaia arrives, she's seriously disgusted by Andrea being a pathetic doormat and tells him that it was his tough badass attitude what made him appealing. So end of their "love story". Andrea of course immediately went back to his old self and you can imagine what he did to Luca and Paolo.
Malaproper: Paolo. Just Paolo. Especially when he tries to pronounce long words ("Asterosterosis" instead of "Arteriosclerosis").
Nerd: Silvano is a textbook example, while Olmo tends on the Otaku variant.
Nerds Are Virgins: Again, Silvano. Until season 5, when he's implied to be the father of pregnant Patti's baby.
Nice Guy: Michele Carminati, Paolo's nemesis, is usually a friendly and good-natured person.
Silvano can be seen as this, although his kindness is mostly due to his shy and naive nature. And when he really gets mad can be as violent as Andrea.
Nightmare Fuel Station Attendant: Andrea, Vittorio and Guido Geller are this in-universe. Also, Silvano: while usually cheerful and naive, when he talks about his mother it can border on disturbing.
No Accounting for Taste: Luca and Alex. She's harsh and spiteful towards him, cheats on him with Anything That Moves and regularly makes fun of his poor sexual performance in front of the other employees. Luca on the other hand, constantly (and unsuccessfully) tries to seduce other women and once he told Paolo that he doesn't like anything about Alex except how "easy" she is and the fact that he's unable to get laid with anyone else.
No-Holds-Barred Beatdown: Andrea is the all-time master of this, really. You name it - any episode featuring him is bound to end like this, whether you get to see it happening or not.
Odd Friendship: Luca and Paolo. The first time they met they hated each other: now they're best friends.
Patti and Alex. Also Paolo and Patti in the episode "Momento d'intesa".
The "ultimate joke" seen in one episode ("Il re degli scherzi", that is, "The king of jokes") consists of a wave of coffee flooding the relax area bursting out of the elevator.
One episode parodied The Matrix, quoting lines of dialogue word for word.
Another episode parodied Final Destination, and Patti avoided a scripted death several times (although this ended up causing chaos). She eventually died by the end of the sketch when the vending machine fell on top of her (a rare case of the view moving).
In the episode Ugly Bitta Paolo, forced to wear braces and red glasses after a car accident, is ridiculized and made fun of by the other workers including Patti, Pippo and Wanda because of his "ugliness". At the end of the same episode there's a reference to another American TV show when Paolo (now without braces and glasses) starts dressing and acting like Gregory House.
Sitcom Arch-Nemesis: the whole unnamed company has the Digitex Company in the same building; in season 4, with the union of the two companies Paolo sees Digitex worker Michele Carminati as this (being also his rival in his selling job) but Carminati doesn't hate Paolo back and wants him to join his working team instead.
Gaia and Ilaria are this to each other; also season 4 has Ilaria and Maria Eleonora.
Small Name, Big Ego: Luca defines himself "tall, charismatic, charming, honest, serious, socially conscious, idealist and a cinema expert". Oh well. He's really kind of a cinema expert anyway. About the rest...
Paolo also qualifies.
Sorry I Fell on Your Fist: When Andrea draws near, you will suffer. And if the sketch isn't over, you will also apologize for bleeding on him.
Status Quo Is God: the trope is generally in full effect, as the only thing remotely resembling a coherent continuity is the change of said status quo between seasons.
However, the trope is acknowledged and sort of deconstructed by Luca in a Season 5 sketch, where Silvano being fired for the nth time invokes in the former an... unusual reaction. Luca spends the whole time of the sketch in front of the coffee vending machine, constantly ranting in Creepy Monotone about how "it's always the same story, nothing ever changes, nothing ever happens", etc. This creeps out De Marinis so much, that he thinks it's another strategy of Luca to help Silvano keeping his job (and it isn't); Silvano then hugs Luca in gratitude, and he replies "You see? Nothing happened." After Luca acknowledged the never-changing status quo, he basically took advantage of it to help Silvano by doing absolutely nothing. At the end of the sketch, Paolo remarks that "You've been there since this morning... I can't see you like this, let's go home". As soon as they leave, the coffee machine falls over. Considering it could have crushed Luca, he snaps out of his depression and says in a surprised voice, "Oh well, so something DOES happen!"
The Stoner: Alex, though we never get to see her stoned.
Took a Level in Jerkass: Patti in season 5. Pregnant Patti is now a histerical, shrill bitch and downright abusive towards Silvano. She's always been the most dominant in their "relationship" but in the most recent episodes she's getting worse and she literally treats him like a dog all the time.
Troperiffic: you've already seen the tropes not related to specific episodes. Keep in mind this is a sketch show. As a consequence, many and brief episodes means many subjects covered, with some episode being based about tropes themselves. You get the picture.
While not at the same level, this is also true for the nameless company. If you are harassing a colleague of Luca and Paolo, they will get you.
Luca: "That's how you treat your boyfriend?"
Digitex Guy: "I'm not his boyfriend."
Paolo: "And those roses?"
Luca: "Pippo, leave this to us, hunny."
Digitex Guy: "There's a misunderstanding-"
Paolo: "Pippo, did this bastard break your heart?"
Paolo: "Then there's no misunderstanding."
*And beating ensues*
The Unfair Sex: if the men are plotting a plan to get to have sex with any of the women, be sure that by the end of the sketch the plan will backfire and the women will react accordingly.
The Unseen: several, mostly related to Paolo, the Anti-Role Model. Paolo's family (his wife Valeria and his sons, Brad and Jonathan) and criminal buddies (Pino, the one nicknamed Budello, as well as Maruska the hooker). There's also Lello, along with his restaurant; the President of the company (the first one and the new one after season 3); Silvano's mom and her old next-door neighbour, Mrs Bollini.
Vitriolic Best Buds: Luca and Paolo are a strong Type 2. Although Luca is usually the most vitriolic one.
With Great Power Comes Great Insanity: in the episode "Direttore per un giorno" ("Director for a day"), Luca's complaints about director De Marinis' bossy ways result in the latter daring the former to take his position for one day. Luca accepts out of pride, and at first everything goes well, but considering Failure Is the Only Option in this series, everything eventually backfires: Luca has only one day to accomplish the task given by the same director he's replacing, and underwhelmed by the responsibility suddenly weighing on his shoulders, he starts treating the workers even more like crap than De Marinis did in the first place, going from idealistic communist to borderline Bad Boss. The episode ends with Wanda (yes,Wanda) knocking him unconscious on the head with a baseball bat, while sporting a Slasher Smile.