"What's the difference between Bookmobile and Book Mower?"
Podcasts — Bookmobile supports them, and Book Mower doesn't.
"Sometimes the app starts back x minutes"
The app must rely on the position information provided by the iOS audio frameworks (it does not "push the playhead along"). Sometimes the position information iOS provides is wrong -- most commonly reporting that the audio is back at the beginning. The app maintains its own "last position" record, but this can only be recorded when the app is in the foreground, or iOS notifies it of an event. Sometimes the app does not get position updates, or notifications that the user paused/played while in the background. In some instances the app can detect that what iOS is reporting is incorrect (like the audio has jumped back to the beginning), and it will try to correct it. It does this by setting the playhead back to the last known position, however, this position might not have been updated for a while.
Things you can do to make the audio position much more reliable:
"This app does not work for me. Should I post a negative review on iTunes to get support?"
That's not really the best option, for yourself*, or for the future development of the app. Please email firstname.lastname@example.org if you have any problems, questions, issues, suggestions or just want to say hi. Your feedback is highly valued, and quite often results in improvements to the app.
*If you post a 1-star review, and then ask for support, you will not get a response.