While most folks write off the April Fool's episode as a waste of their time, I give credit to Matt and Trey for providing a show so distracting that you all may have missed/ignored the clues that it did contain. I seem to remember having seen somewhere that Comedy Central promised that Cartman's dad would be revealed in the April Fools episode even though it was April Fools Day. Then T&P show up for a half hour and everyone goes ballistic. Here's what you may have missed:
When T&P show up in Terror-on (as I prefer to call it) looking for Sally, there is a visitor present in one of the street scenes (the one with Sally in it, right after T&P first see her and say "there she is"). This is the only South Park character in the entire show except for those seen on "lame American" TV.
And let us not forget that the title, Not Without My Anus, may be a reference to Cartman Gets an Anal Probe (My = Cartman), the episode featuring the visitors.
So the clues from Wednesday's episode point to Cartman's dad being a visitor. This would help explain why the visitors, instead of abducting Cartman through his bedroom window, walk right in the front door and drag him down the hall. Shoot, Ms. Cartman probably likes alien sex so much she gave 'em keys to the house...
P.S. In the South Park scene on lame American TV, Mephesto says something to the effect "father is someone" and then the next few words are drowned out by T&P noises. It might help to figure out what he said there, i.e. "someone from another world" or the like...