I could do without the following:
Overuse of pop-culture references/parodies. The occasional timeless reference or allusion to something which has actually become timeless (i.e., "Frankly my dear, I don't give a d**n" or "Mama Mia, that a spicy meat-a-ball!") is fine, provided that the writers don't go overboard with it, but I'll second or third the notion that movies like Meet the Spartans take it too far. There are 2 things wrong with making your show or characters excessively hip: 1) you risk looking like a poseur, like you're just throwing in the references to sound cool; and 2) you end up dating yourself ferociously. I don't need to see a Britney joke followed by a Michael Bay's Transformers joke followed by a Sanjya (sp?) joke. Put some distance between the pop-culture stuff and try to avoid alluding to things that people won't get or give a crap about 2 years from now.
The "smart female, dumb male" shtick. It's not flattering to either sex, because guys don't need to bashed all of the time, and perfect characters who never screw up don't get the laughs. Any male/female pairing or a 'battle of the sexes' scenario which degenerates into "girls rule, boys drool" over and over again I just switch off. Ideally, in comedy both genders should be equally flawed.
Annoying, unfunny comic relief pets. I don't have a problem with animal sidekicks if they're useful characters who actually contribute to the show, like Brian from Family Guy or Roger from American Dad, but I quickly tire of add-on non-human mascots whose comic relief only serves as grating annoyance (i.e., Wonder Dog and Gleek from Super Friends, Orko from He-Man, Slimer from The Real Ghostbusters, Dollar from Richie Rich). I especially grit my teeth when the final joke in every episode skews down to "dumb animal sidekick does something stupid and unfunny, everyone laughs, fade out." Thankfully, this trend kind of died out with 1980's.