Texas which has some of the tougher voter ID laws has found 95,000 non-citizens on the voter rolls of which 58,000 have voted. If Texas has that many, than I would bet states with less strict laws have a lot more. I would suggest this is a problem that should be dealt with by all states.
The 95,000 are the numbers on the voter rolls going back to 1996 who were on any voter roll in any election, and the 58,000 who voted were those who voted in any election over that period. The 95,000 represents a little more than half a percent of the 16 million registered votes and so the 58,000 represents maybe a third of a percent.
So, not to say that there is no problem, but in most systems, especially once that involves maybe a million or more officials in thousands of jurisdictions over dozens of elections over 22 years, I think an error rate of a third of a percent is not such a big deal, especially considering there are so many in the US who may think they are entitled to vote because they have been in the country for years.
More info here: More