Getting off on a dui

What do you mean that the "paperwork was wrong"?  If there was just a misspelling of a name or incorrect street number in an address that would not be substantial enough to warrant a dismissal; the mistake would have had to have been material.

As for not getting read your rights, if you are questioned before being placed in custody you do not need to be read your rights.  If you were questioned after you were in custody and still not read your rights, then anything that you said may not be entered as evidence against you.  However, asking questions incidental to a booking do not implicate someone's Miranda rights; so being asked your name, age, etc, without being given the warning is lawful.