Really, the only ethnicity that can be truly verified is Native American, and only because most (if not all) tribes give out documentation to their members verifying their NA status. Because of this, many law schools will request to see such documentation if an applicant marks down that they're NA. Latino's are probably the hardest to verify because they can be both black and white (and in between, like me). Even though lying about ethnicity is possible, I don't think it's terribly widespread by any stretch of the imagination. People stupid enough to take that risk are probably people who don't have the qualifications to get in on their own, even if someone fell for their phony ethnic claim.