What happens if date gets crossed out and rewritten on a bill of sale or title?

Any change to a written contract should be initialed by all parties involved.  That includes crossing stuff out and writing over it.

The title probably won't be accepted by the DMV.

But..... nobody here knows FOR SURE what the DMV will or will not do.  You will have to deal with your DMV for this "what happens" question

You initial beside where the correction was inserted to acknowledge it is correct.