Acting Unnatural: When the protagonists try to work out who Barney's stalker is, they're told to try to look inconspicuous, and Marshall immediately reacts by acting very strangely, having no idea what to do with his hands, etc.
Arc Symbol: The season marks the debut of the yellow umbrella, which signifies the mother.
Amusing Injuries: Barney is hit by a bus in "Miracles" and breaks most of his bones, although this took a while to recover from, since he's seen in physical therapy in the season 4 premiere.
Broken Record: In "How I Met Everyone Else", Ted's girl of the week asks how Robin and Barney met, assuming that they're a couple. Robin answer this question more than once. (Made even funnier by the fact that they later do date.)
Barney: Really? Sixteen no's? Really?
On the blooper reel, Robin gets to 32. NPH's task during that joke was to sit and count the no's, making sure he kept a straight face.
Brown Note: Lily's paintings turn out to mesmerize dogs and drive birds to suicide.
The Bus Came Back: Trudy, Ted's Girl of the Week during the infamous "Pineapple Incident" in season 1, returns in the episode "Third Wheel". Likewise, two of Barney's GOTW (one from season 2, the other from earlier this season) return in this season's episode "The Bracket".
Cat Fight: According to the "The Bro Code", a bro must always alert another bro when a catfight breaks out.
The end of season 2 was historic according to creators Carter Bays and Craig Thomas for being the first time a television show ended their season in the middle of a word - Barney predicting to Ted that their time as single men together was going to be "Legen... wait for it..." and then cut to black. Season 3 began at the exact same spot, with Barney finally saying "dary."
Chekhov's Gun: Averted in that Future Ted tells the kids outright about the significance of the yellow umbrella of their mother.
Cliffhanger: The season ends with Ted proposing to Stella. She said yes at the season four premiere.
Comically Small Bribe: In "The Goat", Barney hires Marshall to find a loophole in the Bro Code so he doesn't feel guilty about sleeping with Robin anymore:
Barney: I'll pay you. Marshall:(unemployed at the time) How much? Barney: A little. Marshall:(without hesitation) I'll take it.
Complexity Addiction: In "Little Boys", Barney starts to organise a bet between himself and Ted to see who's better at picking up women by thinking up a 'Picking Up Girls Olympiad' culminating in travelling to a neutral city with a panel of international judges. Ted cuts this off by saying that they should just pick a girl and the first to get her wins the bet.
Fauxreigner: In "We're Not From Here", Ted and Barney, inspired by Gael's success with women, decide to pretend to be tourists in order to get girls. This backfires when the girls take them to the south Bronx at night, which Ted knows is unsafe. The girls then admit they are from West Orange, New Jersey and that it's practically New York. Ted then blows their cover by arguing that no, New Jersey is not New York.
Fauxshadow: The mother was at that insane St. Patrick's Day party in "No Tomorrow". This was true for Stella, but she was proven not to be the mother.
Feud Episode: Ted and Barney after Barney and Robin had sex.
Ted: Come on! Let's see the list. Barney: Ted, don't be crass. I would never demean the women that I've slept with by putting their names on a tawdry list. (cut to Barney in the apartment pulling out a scrapbook) Barney: This is a scrapbook of all the women I've slept with. I made it at the scrapbook barn on 7th.
Made even funnier by the fact that according to "Right Place, Right Time," Barney actually does have a list, though evidence suggests he made it specifically for that episode, as he skipped a few numbers and repeated a few numbers.
Freeze-Frame Bonus: In 3x14, "The Bracket", Barney starts trying to figure out which of the women he seduced, lied to, and abandoned is now sabotaging him. We see a slide show of each woman, that gets faster and faster. One of them is Madeleine Albright.
Gratuitous Ninja: In the episode "The Chain of Screaming," the gang gets confused with the report that Marshall's describing, so he just calls it "The Ninja Report." As Barney says, "Ninjas are awesome."
Hair-Trigger Sound Effect: In the episode "Spoiler Alert!", the revelation of particular pet peeves, or spoilers, is always accompanied by the sound of shattering glass.
Heel Realization: After Marshall plays a recording of all the things Ted said at the St. Patrick's Day party in "No Tomorrow", Ted realizes with horror that he had spent the entire night being a complete asshole, and thanks Marshall for setting him straight.
Hoist by His Own Petard: Barney in "Slapsgiving". If not for his mockery of Marshall's slap countdown, Lily wouldn't have given Marshall permission to slap him at the last second
Implausible Deniability: Occurs with Barney in "Miracles" when he attempts to deny the fact that he ran all the way to hospital to see if Ted was okay after being in a car accident. He says that he was actually on the way to a 'very important international business meeting.'
Look Both Ways: In the third season finale, Barney is rushing to the hospital to reach Ted, who he thinks has been seriously injured in a car accident (he was fine). Barney looks the correct way down a one way street, but is then promptly hit by a bus going in the wrong direction. Luckily, he isn't killed, and was in front of the hospital when it happened.
Love Epiphany: At the end of season 3, after getting hit by a bus and almost killed, Barney realises that he is in love with Robin.
Meaningful Name: The club in season 3 episode "No Tomorrow" is called the "Low Point."
Meganekko: Abby, Stella's receptionist, played by the already gorgeous Britney Spears, only got more beautiful by putting on a pair of specs.
Ted: First of all, this isn't one of those "I came all the way over here because I want you back" things. There'll be no startling confession of love, no sweet indie rock song that swells up just as we're about to kiss, none of that crap. Got it?
Especially clever because that is an exact description of the first season finale.
Romantic Spoonfeeding: When Ted dates Cathy, a girl that talks too much (her annoying habit which he only realized when others pointed it out), they are shown cooking together in their being-in-love montage. Ted spoon-feeds Cathy.
Room Full of Crazy: The girl who was seduced by Barney under the alias of Ted Mosby and wrote tedmosbyisajerk.com apparently scrawled "Ted Mosby" all over her walls. It's real pretty, she should be a graffiti artist.
Screw Yourself: Robin claiming she went all the way with her Argentinan self in a dream in the episode "We're Not From Here".
Short-Lived Big Impact: This is the shortest season of the show, but it is perhaps the one where the most important premises of the show are introduced, namely the series' most important Arc Symbol (the yellow umbrella), Marshall and Lily's struggle to find a place they can call their own and a glimpse of the integral Love Triangle between Ted, Barney and Robin.
Spanner in the Works: In the episode "Little Boys," Barney tricks Ted into thinking that he slept with a girl so he could win a bet. When Ted and the girl were about to do it, Ted's mind could only picture tiny Barneys crawling all over the girl. However, Barney was also unable to sleep with the girl because of the tiny Ted dancing on the girl's shoulder.
Strictly Professional Relationship: Ted tries to win Stella and keeps asking her out. She insists that she doesn't reciprocate his feelings, even though the mutual attraction is clear. And as a doctor, she can't really date her patient.
A Threesome Is Hot: Played straight with the guy/girl/girl variation referred to by Barney as "riding the tricycle."
A Threesome is Manly: Completely averted - Barney calls the two-guys-and-a-girl version "The Devil's Threeway" and says that eye contact between bros is / ought to be forbidden.
The Unfair Sex: Robin flat-out asks Ted why he's only mad at Barney about the two of them sleeping together, even though she's just as guilty, but he never gives her much of an answer. Generally sleeping with your ex's friend is just as big of an insult as sleeping with your friend's ex. However, Ted may have looked at it as Barney pulling off yet another one of his schemes and taking advantage of an emotionally vulnerable Robin. There are still some Unfortunate Implications with that interpretation, as no matter how upset Robin was, she should still be held responsible for her actions, but it makes Ted less of a hypocrite.
We Used to Be Friends: Briefly happens to Barney and Ted at the end of the third season, because Barney slept with Robin.