Returning a purchased car...

What kind of car?

But he's screwed

Unless he can show fraud, aren't most used car sales "buyer beware"?

Does TX have a lemon law?

This happened at my old company. The owner called the car lot and asked them politely to take it back. They said no! He said he would give them $. they said yes. This was within 24 hours of the purchase and they were toting the note and had not processed the paperwork. This was for a truck driver we had. Owner worked with the guy to locate a suitable and non rip off deal as he had been riding his bike to work. Within 6months he was arrested and jailed for raping some really young boy. The owner blamed himself as he felt like he facilitated the crime by getting the guy a car. I hope that fricker is dead.

It does say that...

He brought it back same day because transmission is slipping...they said they will fix it...
He is just screwed...

Is he a good employee?

Definitely lesson learned. But if he can show they lied or knew and did not disclose, he may have a case. For example, if they reset codes without repairing, or knew of issues and had a document saying it was "inspected" and nothing was disclosed.

I bought a "new" vehicle from the dodge dealership in BR several years ago, as I'm driving it home I noticed that the passenger door lever was grey plastic while all the others were chrome.
I pulled over in the albertsons parking lot and do a full inspection, several parts and pieces were mismatched( weather stripping on rear window was even missing).
Within 20 minutes I was back on the lot demanding a refund. Dealership wanted to work it out with me and I wasent having it. When I told them I was calling the police to file a report, they were more than happy to give a full refund and return the car I had just traded in.
I guess they pulled a Switch-A-Roo on me after the test drive because I would have noticed the mismatched items.
True story

I'm assuming that this is in Texas?

I don't know about Texas, but Louisiana courts will go out of their way to declare a waiver of warranty invalid to protect the consumer.

If I were a used car dealer, I'd seriously think about videoing my customer talking about the warranty waiver.

Q: Mr. Smith, do you have a warranty with this car?
A: No.

Q: Mr. Smith, what will I do if your car breaks?
A: Not shite.

Q: Mr. Smith, what will I do if you call complaining about some defect with your ride?
A: Well, uh...ummm

Q: Read the line, Mr. Smith.
A: Well, you're going to tell me to go **** myself and hang up.

Q: That's right, Mr. Smith. Do you understand this?
A: [Smith runs out the door]