Gah, you guys. It's way way way simpler than that. Assuming I'm understanding the problem correctly:

1. Open a Windows Explorer window which is viewing the parent directory of the source location which contains all the file subdirectories.

2. Open another Windows Explorer window showing the destination directory where you want to put all the files in one place.

3. In the first window, the source window, in the SEARCH box in the upper right corner, type *.mobi

4. Select all (ctrl-A) and drag them to the destination folder.

5. Profit. I mean, wait forever.

Potential problem you should watch out for, other methods will have the same issue: How to handle the situation where the file names are duplicated. That isn't a problem when they're in subdirectories, but becomes an issue when you want to put them all in the same place. For instance, two different books where the file names are "chapter 1.mobi" "chapter 2.mobi" or something like that.