Probably that would be criminal violations or criminal liability leading to convictions in court. Traffic fines probably do not qualify. (not legal advice)
You can check here if you have further outstanding fines, MVDIS - Vehicle Road Test . Unfortunately only Taiwanese citizens can sign up with the App that would instantly notify you when you get a fine so you could avoid getting a second one.
The complaint I made was that foreign residents don’t get the benefit of being notified of fines and therefore don’t get the chance that locals do to rectify behavior to avoid further fines. He chose to ignore that part in his response. Great if they have actually started to make changes, complain about the app, maybe this time next year they’ll have updated it!
usually based on car registration (camera) anyways. this wont affect your aprc I wouldnt think.
Hit and runs, intoxication, continuous problems towards society might start to be a problem because there can often be an in person vetting of aprc candidates in order to pass. that makes it a massive grey area. but I cant see it being speeding tickets (paid) being the reason for denial.
Also not legal advice. Moreso just practical common sense dealing with them.