All of the following clues from earlier episodes prove that Cartman's father is a visitor:
CLUE #1 - In Cliffhanger (a.k.a. Cartman's Mom Is A Dirty Slut), a visitor appears behind Chief Running Water on the right hand side. Slow motion on a VCR shows this.
CLUE #2 - In Not Without My Anus, a visitor shows up on the left hand side of the crowd scene in Tehran, Iran.
CLUE #3 - Cartman's house address number in most episodes (except for Cliffhanger where it's 28201 which is different on purpose) is 1002 which placed backwards reads 2001.
CLUE #4 - In Pink Eye (which appropriately ran after the April Fool's episode), shows a crashed spacecraft with a visitor hanging out of it on the roof of Cartman's house. You'll also see the address number 1002 in Pink Eye as well.
CLUE #5 - In Big Gay Al's Big Gay Boat Ride, Cartman wears a number 68 on his football jersey. The 68 is probably a reference to 1968, the year that the movie 2001: A Space Odyssey was released.
CLUE #6 - Also in Big Gay Al's Big Gay Boat Ride, two visitors are shown in the first crowd scene of the football game.
CLUE #7 - In Damien and Tom's Rhinoplasty, drawings of visitors are on the bulletin board in the back of Mr. Garrison's classroom. The drawings are placed under the heading "What We Dream..." Perhaps this is a clue to the idea that the whole plot of who's Cartman's dadf is just a dream in Cartman's big-boned head.
CLUE #8 - In Damien, a sign blows around the cafeteria a few times depicting a picture of a visitor with the words "Have You Seen Me?" next to it.
CLUE #9 - Also in Damien, a visitor appears in a crowd scene at the fight on the left hand side.
CLUE #10 - In Pink Eye, a tiny visitor is shown on the shelf at the morgue.
CLUE #11 - In Cliffhanger, during Chef's flashback at the Drunken Barn Dance, we see one cow running away. Remember that cows always run away from visitors. In the other 2 flashbacks, none of the cows move at all.
CLUE #12 - Remember that Cartman had said he was dragged through the hallway of his home in Cartman Gets An Anal Probe. Why didn't the visitors just take him on their ship and give him an anal probe there?
CLUE #13 - Also in Cartman Gets An Anal Probe, the visitors told the cows that they had experimented on many lifeforms and found cows to be the most intelligent. They probably came to this conclusion after realizing that Cartman is an idiot and that their experiment of impregnating Mrs. Cartman to see if they could create a supreme being by mixing the DNA of a human and an alien was a failure.
CLUE #14 - In Tom's Rhinoplasty, Mr. Garrison complains about the movie Contact where he was angry to discover that the alien he was waiting for throughout the whole film turned out to be Jodie Foster's father. A definite hint that a visitor is Cartman's father.
CLUE #15 - Also in Tom's Rhinoplasty, that chick from Species, Natasha Henstridge, was a guest voice. Why do you think that Matt and Trey had mentioned that she played that chick from the film Species? Probably because she played a half alien half human lifeform which is probably what Cartman is.
All these clues lead to the conclusion that a visitor is indeed Eric Cartman's father. Why do you think that Mephesto is goin to get shot in the concluding episode to Cartman's Mom Is A Dirty Slut on April 22? It's a possible government conspiracy to keep Cartman's dad's identity a secret forever. Either that or Cartman was just having a dream and really couldn't care less who his dad really is. We'll see (maybe) April 22. I love a good mystery!