Schools won't care about traffic violations, but you do have to be truthful in your application - disclose in a short paragraph (http://lawschooladvice.com/how-to-write-a-law-school-addendum/) and be done with it. No big deal.
I will add the following warning. Just because a schools says they will consider a June score does not really mean that someone has a serious shot with just a June score. Schools love raising the numbers of applicants to yield protect. I
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