The number we are talking about is not tens of thousands but 500 * 37 or 18500 people or almost tens of thousands.
There are 50 wards in Chicago each ward has about 40 of around 500. so about 2000 precincts of about 500 some odd people If mistake voting was as high as 1% about 33% of that should go for brother Romney. (there were 4 options on the Ballot). A precinct with 500 people all intending to vote of Barry should have about 5/3s or about 2 expected votes for Romney precinct . (498/500)^500 = 0.13479358121 this is the chance that a precinct should have no Romney Votes if no one actually voted for Romney so really not that impossible. 37 / 0.13479358121 = 274.493782774 <-- this is the number of districts that would have to vote No Romney to make 37 districts likely to be error free.
2000 / 274.493782774 = about 7% of chicago districts. Very late here math could be wrong.