I'm having similar issues. I've got several items that are due tomorrow in both the Inbox and other contexts, but they do NOT appear on the home screen. You have to dig down to see the badges, BUT when you go even further into the Context (in this case Home), the application notes that there is 1 item due soon, but navigating further reveals NO action in the particular (Home) context. The item actually resides in "Daily Stuff" - a Project. I thought it could reside in both.
At this time the only badges present are those in the Inbox. Due Soon does not have any badges. I've tried changing the "due soon means" setting to different values with no luck. I thought that this was working previously, but something appears broken.
The lack of badging defeats the whole purpose for this application. It would be nice to see, at a glance, just what needs to get done. Currently, I have to spend time digging down into each home category just to see what's due.