Ok, in order to solve two problems I had to make a change.
First, was that when using the mobile app, it didn't properly show unread posts, because we have been using a cookie based system incompatible with the mobile app.
Second, periodically, peoples new/unread posts would get messed up, usually when accessing BF from two different computers fairly close to each other in time, or bouncing between a mobile phone access (standard site, not Android App) and their PC.
In order to fix this, I have changed vBulletin to track unread posts via the database. The downside is that everyone's read posts went away after I made the change.
You only have to do this once, but after you have read the threads that are really unread, you can go to the navigation bar and click on "Quick Links" and then on "Mark Forums Read" and it will mark everything read and then should work fine from that point forward.