We bought our house in 2004 and have recently discovered the tile the previous owners had installed was done over linoleum and now has be replaced. Do we have any recourse?? Are they liable for having it incorrectly installed?

It's about 4 years too late to do anything about this now. Possibly if you had hired a home inspector prior to buying the home it could have been discovered as being improperly installed. Right now, you're stuck. Sorry.

We DID have the house inspected, but there was no way to tell that the tile had been installed over linoleum at that time. Was this something that should have been disclosed to us?

Not necessarily. That was not a problem if your home inspector didn't catch it. The tile is now coming up. At the time I don't think it really mattered. Something like cracked beams would have been discovered by the inspector and needed to be fully disclosed by the sellers. Tile improperly installed wouldn't fall under the disclosure umbrella as it is not a structural defect.