Random Skips

Len, Does it happen when there is heavy bass? Does it happen when you are playing quietly or only at high volume? I can't believe a Rega cartridge would be incompatible with their own turntable but you could have a defective cartridge. If the cartridge is too stiff for the mass of the tonearm (low compliance) the tonearm will pop out of the groove with the right bass note. Other possibilities are, your anti skate mechanism is sticking, your tonearm is running into the cuing device, your tone arm bearings are defective, your turntable just hates you. Also, make sure the table is perfectly level and the cartridge is aligned correctly. 
To check for a defective cartridge you will need a test record with resonance test tracks. Defeat the anti skate device and see if the skipping stops. 

Good luck
Mike    

Anti-skate is notoriously imprecise, varies across a side, and even varies (as Mike alludes to above) depending on how much bass energy there is on a track. When it skips, does it always skip to the outside, playing the same bit over and over again? Or does it skip ahead to the inside? 

If it skips out, decrease anti-skate. Skips in, increase anti-skate. 

If its 50/50 well then we need to look deeper. But this is a good first step.

The bass is shaking the table. 

not to be your nanny here but you may also want to reconsider your listening levels at those levels (100db) your damaging your hearing. There is no coming back from damaged hearing. 

Sorry if I'm treading in a not your business area, but I do come across people who just don't know what the limitations of human hearing are and when damage starts from excessively loud sounds. 
above 85dba we start to get permanent hearing loss. your ears though not mine. 

https://www.nidcd.nih.gov/health/noise-induced-hearing-loss