How to circumvent game breaking bug in GTA: San Andreas (PC)

I have never encountered the 'skipping' bug you describe, but in terms of getting 'misses' on beats, there may be another solution:

The game's timing for the rhythm sections, (especially the Lowrider challenge but also when Dancing), is off by a fair amount. Even on the old PS2 version running on a CRT (with little to no image preprocessing), the off-beat display of the buttons in the sweet spot is noticeable.

From my years of playing, the beat seems to be about 0.4 of a second off from the music in the Lowrider challenge, and closer to 0.2 off in the Dancing sections. You need to almost ignore the beat of the music, follow the incoming buttons, and press slightly after when you should.

Take this terrible MS Paint example I drew up in about 30 seconds:

Normally you would push to the beat of the music, which (ideally) would be represented by the middle of the blue circle. However, you need to hold off just slightly enough to press the button as it leaves the circle.

Personally, for years I actually muted the game during the Lowrider challenge as I found it that distracting, it took me a while to be able to pass with the music on.

As always, practice makes perfect, so save beforehand and just repeat the challenge over and over. Pattern memorisation also comes into play, as the buttons are in the same order every time. So keep at it and you'll get it eventually!