Is there a way to know if an original DVD has been copied?

No.

There’s a new technology called Cinavia that watermarks the dvd if copied. I believe it claims to show which DVD it was copied from (although don’t quote me on that). Either way, people have found ways around it.

If you’re asking whether, if you rent a DVD, they’ll be able to tell whether you copied it after you return it, the answer is no. I don’t think it’s enough of a concern.

Yes.
@MyNewtBoobs is correct in the technology. It has been started to be utilized in some Blu-ray releases. It is an imperceptible audio watermark that if not properly written or detected in the playing device will stop the audio or video completely.
There are alreary simulators of this available for the various decrypter and buring drivers.