[PatNY]

I solved the issue.

First I ran a debug but there was nothing in the log that suggested an issue. It merely said the book was added in 1.4xxxxxxxx seconds!

Hmmm, so I thought maybe there was something in the source book files themselves. These were a group of books a friend of mine had given to me. So I added from another totally separate group of books as a test and, sure enough, the date was correct, so obviously the source files were the issue. Upon further testing, it appears the issue is in the OPF file that came with each of those books. It had this line in it:

<meta content="0101-01-01T10:00:00+00:00" name="calibre:timestamp"/>

So, no problem. I will just pay closer attention to source files in the future when I add books and manually change the "date added" to the current date if necessary.

Thanks to ducks and Kovid for your help.