The mistakes on the “registration” follow the register, not the vechicle. Like someone else mentioned, if you lapse your reg or insurance the DMV “fines” your name, not your car. that means they cant alter any new/current vehicle under their name.
Selling the car to someone has nothing to do with the mistakes they made.
Once the title is in your name, as long as your dmv records are free and clear your good to go.
A friend of mine messed up and he got his plates suspended for over a year! He sold the car to his friend/neighbor for a 1$ and they registered it and insured it for him, he just made the payments to his friend. it was his only car so he needed to get to work somehow. He waited the year for the suspension, and bought his car back. lol
but yeah, make sure if your unconfertable taking adivce from internet peoplez.