Via Hot Air, there are two reports from precincts that election night tallies were wrong. In one instance, a man credibly claims that Romney was awarded 20 more votes than he actually received. But Santorum said on Fox News last night that 21 Romney votes weren't counted in another precinct, so Romney still has the lead.
In the end, we'll never really know who won more votes in the 2012 Iowa GOP caucuses. Maybe Romney lost Iowa by dozens of votes, maybe he won it by dozens of votes. We'll never know.
It is very common for results to shift by hundreds of votes following a typical election, while election officials conduct a "re-canvassing"--i.e. double-checking to make sure they relayed the correct vote numbers from the voting machine to the state election board. It would be very surprising if there were only two errors in the entire state of Iowa.
In the 2008 Minnesota Senate race, for example, Norm Coleman's lead "dropped" from over 700 votes to 215 votes just because of typos (more than 2 million votes were cast in that race, compared to just 122,000 in the Iowa caucuses). Even before a Wisconsin official found that thousands of votes hadn't been counted in a recent state supreme court race, the vote tally was seesawing back and forth as errors were discovered. Again, these were all errors discovered during the re-canvassing period, before any recount occurred.
The GOP caucus is conducted entirely by Republican party officials and volunteers. There is no formal re-canvassing process,* and there is not an opportunity for a recount. It doesn't matter in terms of delegates who won more votes in the Iowa caucus, but it does matter for bragging rights. And an 8- or 9-vote margin of victory is just so small that we can't know for sure that Romney really won.
Update: See Nate Silver's new article: "Iowan Casts Doubt on Winner of Caucus."
*Update II: Iowa GOP spokesperson Nicole Sizemore emails: "The state GOP certifies the results within 14 days of the caucus. During this process we receive the official forms from all 1774 precincts that have the recorded results, and which we use to certify the results." So there is an opportunity to correct mistakes made while relaying the vote tally to the state GOP, but if a mistake was made on the official form, it seems there is no process to correct such an error.