Those definitely look like water spots to me. @oldturkey03 has a lot more experience with this than me, but my guess, assuming the spots aren't on the surface, is that there's a good chance you could disassemble the screen and clean the individual layers of polarizer, LCD and backlight. You just have to be very careful to reassemble everything in the exact same sequence and orientation you took it apart in, and of course whatever you do, don't apply too much pressure to the LCD; if you crack it, it's pretty much game over.
Thank you very much for your insight. I will try it out if I decide to keep it. I now know that if I do keep it, there is a good possibility of repair.
@bbcski I concur with @dadibrkeit. Looks like stains on the diffuser. You can fix it by disassembling the complete panel and cleaning the sheets. 2 things to be careful of. Do not bend the panel, secure the driver boards that are attached to the panel, with some painters tape. Next is to mark the order and the direction of how the sheets are inside the panel. They have to be re-assembled in the same order and direction.