I bought a used car seven days ago that I had checked at a different auto shop. They told me there were issues that the dealer says are not covered under my warranty. Can I return the car if I am not satisified with their response.

Not unless you have a return policy in the contract that you signed. Before you buy it, is when you need to have it inspected, not after.

Warranty is very specific, many things on used cars are not covered under warranty, so get your copy of the warranty out and see what is or what is not covered.