And when we first meet Frink’s son, he’s in a remote control plane. When it goes out of control Frink says “My wife is going to kill me.”
Ah, I forgot about that one. So it is inconsistant, but not neccessarily for the reason you had earlier. 
The real ‘problem’ is that they’ve spent so much time filling in characters’ backstories that it’s bound to contradict some of the stuff we already know. For the sake of my own sanity, I disregard a lot of the throwaway jokes as non-canon anyway. (The fact that I’ve given it this much thought may prove that, in sanity terms, I’m bailing water with a thimble.)
Then there’s the stuff that doesn’t contradict the other stuff, but doesn’t quite make sense anyway - like when they revealed that Edna Krabappel hasn’t been worn down and jaded by years of teaching, she’s just been worn down and jaded by a few months with Bart Simpson. C’est la vie, I guess.