After watching a TV show you've previously watched on Hulu until the very end and then letting it auto-play to the next episode (this was before the auto-play was broken *a current issue* and is still an issue now that it works off and on), the next episode picks up with about a minute left of the show. It doesn't start from the beginning. This happens even if you've watched the next episode all the way through at a previous point in time. So it's not as if it's picking up from where you last left off.
Before posting here I sat and watched this happen multiple times. You could go through 5 episodes in a matter of minutes because of this issue.