My problem may be that I'm closing the app instead of backing out of the task detail screen.
My issue with the badge update was that it wasn't reflecting what was currently due. It was pushing badges for tasks that had been completed or in another instance, a task due the current day that I changed the due date for, but again that may be because I was exiting the app without letting the sync run
On the iPhone, is the sync on edit limited to certain edits? I've had a couple of instances where I've changed the due date from the current date to a future date or completed a task but still get a badge pushed to my phone as if the edits weren't saved.