I don't think you can cite this as a flat-out error, so much as an alternate interpretation of the show. And no disrespect to MissM, but even a Disney source doesn't settle the issue in my mind.
When Disney says it's one family, they clearly don't mean that in the way it would normally be interpreted. They're just coming up with an easy way to explain what happens in the show without delving into metaphysics. It doesn't strike me so much as a definitive answer to this question as it seems the kind of response you'd get when you ask about the plot of a movie that's hard to describe.
("Well, there's this family, see...well, I guess they're one family...it's not exactly clear in places..." *other person starts getting glazed eyes* "Yeah, it's about this family...")
It's clearly not one family in the literal narrative sense (they may not even be the same characters from scene to scene, except for Dad)...so you can say it's one family in the archetypal sense (The American Family), or in the fictional characters never age sense (the Mickey from Steamboat Willie is the same Mickey seen today), or in the "jeez-we're-having-fun-so-don't-think-too-hard-about-this" sense. All of which I can respect. Nothing wrong with any of them. But they're no more definitive in my mind than the four families idea.
