The gate staff should just let anyone onboard with a legit ticket or a sufficient story about buying one.
Sure, some people might get a free ride, or a few legit ticket holders can't get on because the plane is full, but overall, most passengers end up happy.
Simple things like "the pilot can't log in to the HR system so he gets paid for the flight" should be fixed with a combination of process changes and "let's just fly now, make paper records, and fix the computer records later"
Communication systems should have a backup of a large box of walkie-talkies in every airport so that, for example, the baggage staff can radio to the pilot to let him know they are done loading.