While it was noted that in that occurrence it wasn't in front of the family, it should also be noted that this was the third episode aired and the Homer in that episode was quite a bit different from what his character would become known for(in fact in the episode he changes character several times, and none of them are true blue Homer). This recent suicide gag was very uncharacteristic of the familiar Homer, and really just another example of the writer's willingness to throw away all characterization for the sake of a joke, or at least what they think is a joke.Yes. He gets fired from the nuclear power plant because of his incompetence. He can't find a job, so he ties a rock to himself and tries to throw himself off a bridge.
I guess what I'm trying to say is that the inconsistency was forgivable in the third episode, but now it's not because of what became established through the years. But this has happened with so many other characters, and is a major reason why the show is pretty much unwatchable now.