I just did a detailed study of my LCD, and confirmed what others have said - mine doesn't have a film, either.
I'm not sure about the D300, but it's common to have a protective glass (or plastic) over the actual LCD display. It's also possible that there was some protective film there that wasn't removed in the manufacturing process. That you saw this problem with both cameras from the same retailer indicates there may be a "batch problem" that you're experiencing, and Nikon needs to address.
Just because none of us see this film, doesn't mean you're not having the problem.
Do you know anyone nearby who has a D300? Can you visit him and see if his camera has the film visible or not? Can you go to another store that might have the D300 from a different batch? Maybe even the display model at your camera store? They usually don't trade those out. Those are usually among the first cameras that the store receives, so they should be from a different production batch than the two you recieved.
Given some of the other issues here (early Nikon response to the D70 Blinking Green Light of Death - BGLOD - to the D300 Battery Depletion Syndrome), Nikon's first response will probably be denial of the problem. If you can verifty that your camera is different from other known good D300s, be very insistent that their technicians evaluate the LCD screen.
Oh... Can you take a picture of the D300's LCD screen with your D80, that shows the film you're talking about. That might also help Nikon evaluate the problem before they ask you to send your camera. "A picture is worth a thousand words" after all.
- Arved “If you like the way it looks, take the picture. You don’t have to be a portrait judge to know when something looks good. You simply have to develop good taste through learning the basic principles of good composition and lighting.”-- Monte Zucker