Deadpan Snarker: Surprisingly Balki, especially towards Larry's penchant for blowing smoke.
The Ditz: Mary Anne; although she borderlines on Genius Ditz territory in later episodes as part of a recurring gag in which Mary Anne will occasionally say something smart, which causes Balki, Larry and Jennifer to look at her strangely, only for her to explain how she knew it.
Flanderization: Especially Larry Appleton. As time passed he became more centered on the arrogant-knowitall-cityboy-with-a-scheme aspect he occasionally showed in the earlier episodes, resulting in the show becoming too formulaic where Larry cooks up a plan (where he would say his Catch Phrase ) and then the rest of the episode will show how things get fouled up.
Foreign Queasine: Played straight through as a running gag in the series. Numerous times throughout its run, Balki Bartokomous will often make and serve dishes from his home country of Mypos to his cousin Larry Appleton, that contain such bizarre (and vomit-inducing) ingredients such as yak bile and the bladders of sheep and pigs. The season three episode "Come Fly with Me" centers on this, as Balki and Larry's flight attendant girlfriends Jennifer and Mary Anne get sick from eating Halkidikis (coincidentally sharing an alternate spelling of a Greek peninsula), described by Balki as the "travel food of Mypos", whose primary ingredients are the standard ingredients of milk, eggs, flour and honey, and goat spleen with mold aged to the point where it developed green fur on it. This is inverted however in the season three episode "Just Desserts" with a dessert known as the Bibi-babka, which contains typical dessert ingredients and which Larry attempts to market (though he tries to make it in such a rushed fashion that they explode because they weren't made with love and care).
Friends Rent Control: A photographer, a mailroom clerk/cartoonist, and two flight attendants could not possibly have afforded a big Victorian house in Chicago's Old Town neighbourhood.
This was late in the series as Larry and Balki were shown living in a regular apartment through most of the series, and their promotions to editors in season 7 would've helped.
Happy Dance: Balki would break out into this on occasion, dragging Larry along with him
It was a specific dance Balki called the "Dance of Joy". At the end of the dance, Balki would be holding Larry.
Hustling The Mark: Gorpley once took all Balki's money in a poker game, so Larry gets in on the next game to try and hustle Balki's money back. Larry uses his reputation as a Know-Nothing Know-It-All to hide the fact that he is an excellent poker player and destroys Gorpley.
Identical Stranger: Following their break-up, Balki and Mary Ann date carbon copies of their exes. While they are in complete denial about their new partners (though Balki later admits it after slipping and calling the other woman "Mary Ann"), they each immediately recognize the similarity in each others. The episode ends with them getting engaged.
Jerk Ass: First it was the pair's employer and landlord, Twinkacetti. Then when they got jobs at a local paper, such reins were passed on to Mr. Gorpley.
Never Win The Lottery: Larry wins the lottery, but loses the ticket when Balki donated some clothes to charity, including a suit that Larry hid the winning ticket in. After getting it back, it turns out Larry had missed a couple numbers and won a lesser prize.
No Celebrities Were Harmed: The "bibi-babka" episode was a retelling of George Papashvily's epic tale, from his autobiography Anything Can Happen, of he and his friends making and selling khinkali dumplings to restaurants. They pulled it off successfully once.
The Not So Harmless Punishment: A Myposian aquaintance of Balki's challenged Larry to a duel once. Larry accepted after Balki tells him it involves boxing the loser's ears. Then, Larry realizes that in Mypos, "boxing one's ears" means putting the ears in a box.
Paranormal Episode: There was an episode where Larry and Balki discover a ghost in their new house. There was also an episode where Balki turned out to be an alien, but in that case it was All Just a Dream.
The Rashomon: And when asked where the truth would come from, everyone pointed to Balki.
Re Tool: The show was overhauled in the third season, with Larry and Balki getting new jobs in a more glamorous setting (a big newspaper instead of the small store they'd been working at before), new supporting characters including Mr. Gorpley and Harriette, and a memorable new title sequence with footage shot on location in Chicago.
Shaggy Dog Story: Larry would often tell these to Balki (though "a look...into the future!") to either convince his cousin to aid him or spill the beans on something. In any event, once Larry got what he wanted, things don't go as planned.
Show Within a Show: Later seasons featured parody clips of the show Laurel and Hardy, with the titular characters being played by Balki and Larry respectively. Mixture of Type 2 and 3.
Twisted Christmas: In the first Christmas episode, various problems get in Larry's way of taking Balki to his folks' home for a "real Christmas". In a later one, Balki invites sour-puss Mr. Gorpley to his and Larry's holiday shin-dig, where he quickly infuriates the other guests before offering his tragic backstory. In both cases Balki then subverts this trope by being...well, Balki.
You Look Familiar: Sam Anderson (Mr. Gorpley) appeared once in the first season before returning for his more recognized role. Belita Moreno appeared occassionally in the first two seasons as Mrs. Twinkacetti, before playing Lydia later on.