How does a PFD handle unphysically abrupt changes in the parameters it's displaying?
Generally, PFD will smoothen the indication for most of the indicated data.

I don't know any 'legal' requirements for it, but as you mention, basic ergonomics require it.

I have first hand experience with Garmin G1000, so I'll try to explain its PFD behaviour as an example. (It's a bit hard to capture and post a video).

Most (if not all) 'graphical' indications are filtered with the rate (characteristic frequency) consistent with the expected rate of change of the relevant parameter: pitch/roll quickly (but still noticeably, about 0.3 s), airspeed moderately, engine temperature slowly (3-5 s). Digital only indications (say, battery voltage) are also filtered, and in addition their precision is limited such that the updates didn't happen too frequently (e.g. round 0.5 V).

The filter seems to be a second-order low-pass in most cases. For some parameters, notably the indicated airspeed, it is underdamped, which means the indication overshoots slightly for abrupt changes, and generally tends to oscillate to and fro for normal changes. This provides faster response while still being smooth.

An abrupt, unrealistic change of parameters per se doesn't cause a fault for PFD. It's just filtered as usual. However, significantly out-of-range values will fail the indication, but only temporarily, until sensible values resume. Generally, it's the job of the peripheral computers (ADC, AHRS, etc.), as well as of the integration unit (GIA), to detect faults and convey them in special messages. PFD is, after all, just a display.