L.L.
You can sell your car as is...after you buy a car, you have a small leeway of time before you have to register it, so that's on the buying party.
However, make SURE you have them fill out the transfer of title (the card on your title) and mail it in RIGHT AWAY. Here's my semi-horror story.
I sold my car a few years ago for 600 (it was old and worn) and filled out the card, had them sign it, sent it in, and was done. I didn't keep any record of who I sold it to, etc...it was a cash sale to (just being honest) an illegal immigrant.
A few months later, he was in a hit and run accident with it. He never went to re-register the car, so the car he hit's insurance company called me. I was the only name they had. I have this lady from the insurance literally calling all day long, harrassing me, threatening me, saying they're going to sue, etc...and I did NOTHING wrong.
Finally, I called the police to see if the car came back to my name...gave them the plates...it didn't come back to me, it came back to him. So, the insurance company's just going off whatever screwed up system they're using...but the police couldn't give me a name. So I had the insurance lady call our police to request the information, and the police kindly informed her if I EVER heard from her again I was going to sue HER for harrassment. It was seriously the worst day I'd had in such a long time...
The only reason I say all this is because really, in used cars sold from seller to buyer, things happen. So do everything you can to protect yourself!