Oh - and scientists who know every field of science! Dana Scully was the big one for me. The woman is a medical doctor! She should know medicine - and likely only know one or two fields of medicine well, at that. She might have a decent general knowledge of biology and chemistry, but she would be no expert in either one. But she constantly makes pronouncements about every science - hell, her thesis was rewriting Einstein!
On similar lines, Doctors who can treat any alien. There's no such thing as a Doctor who even knows every field of Human medicine well, but in sci-fi Doctors usually not only know every field of Human medicine, but everything about dozens of alien species as well. You could spend a lifetime of studying and never cover a tenth of all that.
Word. That got on my nerves.
And to add to that: the fact that both Mulder and Scully weren't allowed to grow, change or evolve... unless forced to. Only when Chris's hand was forced, did those two ever grow (at least from what I could tell). Once the audience he gave a damn about left, he was left with the one he didn't really care for. So the show was forced forward. But once it came back, everything good was taken away and we were left with the same old non growth and evolution.
Which leads me to another pet peeve: break ups that lead to nowhere
It was all done for teh DRAMA (which is another thing I really don't like -- meaning drama for the sake of it, shallow plots that lead to either unsatisfying conclusions and/or ones that lack anything meaningful).
And then it lead to another thing I dislike: having the characters get back together for one night for comfort and have it lead to the female character (in this case, Scully) getting pregnant. The entire episode, Plus One, was nothing more than a cheap plot device leading up to that. Which was eventually revealed in the final episode, My Struggle (to not throw things at my tv) 4.
The worst part of Plus One: The name of the motel... it was a nod to something in the bible. The story of St. Rachel (being that the woman dies in childbirth). It made me sick. That the character (Scully, herself) would possibly be put at risk. I really don't like stories that resort to cheap angst either.
Another thing I'm no fan of... character's children that pretty much turn out to be evil (William/Jackson, Mulder and Scully's kid was this). Such a cheap plot device.