How inaccurate do you think national popular vote totals are?

[ShamDam]

Looking at the Wikipedia page for the 2012 election, I was thinking about Barack Obama receiving 65,915,796 votes, and thought to myself "there's no way that number is precisely right." Human error across the country, and just the nature of randomness, surely means that the number cannot be accurate to the vote. Misplaced ballots, misidentified ballots, faulty precinct practices, stuff like that has to go wrong across the country on some scale.

So the question is, how inaccurate are they? Has any research been done on this? I think one benefit of the electoral college is that it prevents these things from really mattering. If we did elect Presidents via a national popular vote, and an election was super close, I think a nationwide recount would be bonkers.

I feel like it's kind of a weird question, but have at it if you have thoughts on the matter.