Its been a while, but the way I remember that movie it was multiple prospective sperm donors (six?). If sperm from all 6 were used, it would essentially be a crapshoot which one actually managed to merge with the egg. Without genetic testing (this movie was made in the 80's when that was new and expensive) it would be difficult to tell which one "won".
The additional wrinkle was that there were twins. As Fraternal (not identical) twins, that means two different eggs merged with two different sperm. So it would be possible in that scenario for twins to have different fathers. Technically these twins would be half-siblings. Again, it would be tough in the days before cheap genetic testing to figure out for sure which of the 6 was your biological father. But if you went to visit all the donors, you could perhaps make some educated guesses. So that's what they did.
At least that's what I told myself while watching it. According to the Wikipedia blub they somehow spliced material from 6 donors. That would be scary madness even today. We don't know enough about how multiple genes interact to confidently create a working human that way. It also claims the twins happened when the embrio split. That can happen, but if it does both copies have the same genes, so you get identical twins. So clearly that didn't happen.
So basically the given science for the movie is complete nonsense. I'd advise either ignoring it, or using something akin to my rationalization so you can get on with enjoying the story (which was kind of fun).