...the way I see it, 1980s VCRs got it right the first time with "+00:00" on a flashing VFD display, taunting you to re-set it again - all because someone unplugged it by mistake (dumb-question: why couldn't VCRs get the time from the TV signal?).
(What I mean, is that I think all systems (hardware and software) around the world just should standardize on flashing a message simply reading "+00:00" for all unintentional clock states. Clocks are one thing that I feel should not feature graceful-degradation - consider that's the whole origin of the idiom that "a stopped clock is still correct twice a day"; I'd very much rather a stopped-clock's hands broke-off entirely instead of risking it being misinterpreted by people who think the clock works just fine but they themselves have a bad case of saccade chronostasis[1].