I found this 1957 D in my stuff that had a thin film over it. For fun I soaked it. The film came off all in one piece after a couple of days. Under the film the surface looks as though it was just recently minted.
There are probably many different possibilities. I don't think it was tape. But I can't swear to it. Here are two shots of what I removed. One is with a green background and one with orange. It is completely irrelevant, just interesting.
Not as far as I can tell. It had this partial film over it. I soaked it for a couple of days and then just lifted it off. The surface under the film looks to be MS. You can see that the rest of the coin sustained normal wear. I didn't get any lift on the obverse.