There were two unusual lines, both confusing and concerning, on Jonathan Latimer’s vote-by-mail ballot: "MAIL 6619” and “BROWN UNIVERSITY.”

Neither line is part of his actual address in Middlesex County, N.J., and so Mr. Latimer, 76, who went to college in California many years ago, was concerned the erroneous and random insertions threatened to invalidate his mail-in ballot for November’s midterm elections.

If the address on his ballot didn’t match the address the state had on record, he wondered, would it be counted given New Jersey’s strict vote-by-mail requirements?

Turns out, Mr. Latimer is not alone. More than 43,000 vote-by-mail ballots were sent out, and the Middlesex County Clerk’s office estimated that “a large percentage of them” contained erroneous address information, though they were not able to give an exact number of affected ballots.