There are a couple of explanations being floated. First of all there where two votes, not just one, and if you wanted to vote 'correctly' against A13 you had to vote NO on the first vote and YES on the second (or vice versa to support A13), The people who voted 'wrong' voted either NO to both or YES to both.
Secondly apparently the order of voting was changed at the last minute (there where a whole bunch of things being voted on that day) so people who had written down what they where going to vote on each issue (NO,NO,YES,NO,YES,YES,NO etc.) and missed that the order had changed would end up voting wrong. Ie. they knew they wanted to vote YES on issue 27, but issue 27 was actually the 28th item voted for that day. At least two MEPs in Sweden are using this excuse.
But basically a bunch of MEPs just didn't think it was that important to pay attention to the details, phoned it in, and screwed up badly.