Diane and Istmus,
I have an identical problem, and I wanted to add some info about my experience in case it helps. At least it should help people from wasting as much time as I have...
My experience is essentially identical to Istmus. I also HAD several POP accounts (plus I use an IMAP account for work in addition to the POP account to do occasional maintenance on my account on the server - we do not use exchange here). I started having the same issue as Ismus describes. Tasks are ok if you are in the to do window and just click the task list, but if you look at the entire to do list, then flagged emails are the issue and cause the problem.
Note that all the emails are flagged correctly if you find the email itself, this is just a viewing issue with he to do list and the to do bar.
After many things done including copying .pst files, deleting and restoring email accounts, running command line switches to reset the to do bar, clean reminders and so on, nothing worked.
So then I gave up and started a new profile and started with a single POP account for my most pressing concern, my work email. With just that one account, the to do bar works as intended, even when using my old .pst file. It loaded and everything looked good (which is good because that is where everything I need to be reminded about is!)
However, once I added a second email account the problem immediately reappears if the .pst file has any emails flagged. I tried this on two of my other email account and one doesn't have any flagged emails and that didn't cause a problem. However, as Istmus reported, as soon as I flag an email in the account, I get blanks for the group that includes the due date of the just flagged email. If I unflag, the problem clears. If I re-flag as due tomorrow, then tomorrow's group on the to do list has the issue of being blank.
Further, even when I deleted that account and added a brand new account with a fresh .pst file, the problem is still the same. So then I figured it had to be a bug, and my guess was it occurs when you have more than one account. So I went looking for Diane whose information has helped me countless times over the years and sure enough here we are.
After reading this thread, I went to look at the bug report, and I wish I had seen that yesterday. I see my conclusion is correct that it involves two accounts, however, I want to mention that the info on the microsoft page about the issue says the problem occurs "If you have two different Exchange accounts (including Outlook.com) in your Outlook 2016 profile..." however I have no exchange account as I mentioned so this appears to apply to pop accounts also.
As for the workarounds, sorting by anything other than due date appears to work and all items are shown, however by due date is really the only useful sorting option I use so that isn't too helpful.
The best workaround I found is not showing in groups (which is ironic since I hate groups for anything but the to do list sorted by date!). This is one of the MS suggestions but they are referring to the task window itself which I rarely look at, I just use the to do bar. The good news is not showing in groups on the to do bar also works to clear the problem, just without having the overdue, today,tomorrow, etc groupings by due date which I like but now this is a minor annoyance instead of a major problem preventing me from know what to do! haha.
I am back an running for now, when I have the chance I will add back in my other email accounts and see if things stay the same.