many times, after a skater makes a mistake, they try to gain back speed with less than ideal pushes to get to the next element or musical cue.
Ultimately it varies with each skater and mistake, and it's a judgment call on your end, but it's true, IMO, that a skating skill score should be affected by mistakes in most cases.
Definitely. It depends a lot on the mistake.
First, not all errors are serious. And some are serious in the sense that they result in a significant loss of points but are not disruptive (e.g., an underrotated/downgraded jump with a moderate touchdown of the free toe on the landing but no loss of balance -- a casual viewer might not notice at all).
From the current ISU Singles/Pairs guidelines,
ISU Communication 2788:
Program Components evaluation
If a program contains 1 Serious error, the maximum score for each program component is 9.50. If a program contains 2 or more Serious errors, the maximum score for each program component is 8.75.
Serious errors are falls and/or mistakes which result in a break in the delivery of the program. This break can be minimal or more pronounced and noticeable. These errors must be reflected in the mark awarded for each program component. The consequence depends on the severity and impact they have on the fluidity and continuity of the program.
When awarding Program Components when there have been serious error(s), ensure each mark accurately meets the criteria for that range of mark even with serious errors.
This is then restated on the final page with the colored PCS chart.
Not directly related to PCS, but there are also guidelines about how errors affect maximum allowable GOE (see p. 16 of the document linked above).
I.e., if there are other positive qualities, a judge should reward those first up to +2, and then take the necessary reductions to end up with a final GOE that would be negative but not necessarily -5.
I mention this only because many of those errors that require starting GOE no higher than +2 before reductions are things that would not be disruptive or visible to casual viewers.
So if you're just watching and not looking at the protocols, you might see "Skater A had two mistakes! I saw them! Skater B was clean!" and think that Skater B therefore deserved higher PCS.
The judges might think "Skater A had two serious visible mistakes, but everything else was excellent. Skater B had a lot of small-to-medium technical errors, and their basic quality was just in the "Good" range, not Very Good.
So Skater A ends up with PCS in the 8s, Skater B with PCS in the low 7s, and viewers who judge technique mainly on the presence or absence of obvious disruptive errors think the decisions were made based on reputation. But the reputation may be based on actual technique that's harder to appreciate on video or without significant training.
That would be most relevant to the Skating Skills component, which is where technical quality would be most reflected in the current 3-component setup.
For the other components, a disruptive error like a fall is more likely to disrupt the performance quality or timing to the music, or possibly the composition if the skater has to abandon choreography to catch up to where they need to be for their next element. Or it might not. Not all falls are equally disruptive, and in rare cases skaters are even able to work the fall into the performance quality.
My favorite example (albeit not from eligible competition or IJS era):
https://www.youtube.com/watch?v=isA3CIbU9dI&t=3m48s
Another example from 6.0-era competition:
https://www.youtube.com/watch?v=ptnALdiKPuY&t=1m23s
That one is interesting to watch because there are a lot of serious technical errors on most of the jumps, but only 2 or 3 would count as disruptive. How would you rate the Composition and Performance of that program against a skater with no falls, clean triples (but no 3A attempt), and not much creativity or musicality?
