News reports now are that the votes from several Iowa precincts are missing and won’t be found. It seems likely there would be limited places where the votes could be. Outside of deliberate destruction, which seems improbable, how could the votes actually be unrecoverable?
Caucuses aren’t formal votes. People sit in rooms and pass ballots to a coordinator, who counts them and then phones the results in to some central location, which reports it to another central location, which reports to the party headquarters. I’m not sure of the exact number but it’s a chain of links.
That gives several points along the way for totals to get lost in all sorts of ways. I don’t know what’s done with the original ballots, but I imagine that most of the time they’re thrown out.
Nobody cares. Iowa caucuses are unofficial preferences. They count for nothing. The actual delegates are chosen by another process. Romney’s “victory” gave him the right to the same number of delegates as Santorum. A few votes here and there don’t make any difference. It’s not a vote, so there can’t be any voter fraud, and the procedures don’t need to be any more rigorous than for president of the senior class at a high school.
Actually, paper ballots are involved in the Iowa caucuses. From Wiki:
I said exactly that. And I said the results were phoned in without the paper ballots going any farther. What’s your confusion?
It’s not exactly a ballot in the way most people know – where you fill it out, scan it in a machine, etc. It’s really just tossing a paper in a hat with a name written on it. Iowa caucuses are very informal that way; it’s not like during normal elections when you have a formal ballot, absentee voters, possibilities to recount, etc.
Who gets to name the hat?
Harry Potter.
I strongly suspect that a magical, telepathic, talking hat that can see into the wearer’s soul would be a far better system for selecting candidates. 
OTOH, I think you’d get an awful lot of “Better be…Slytherin!”