As Joseph said, spetsnaz was not 'all one unit'--there were army and navy branches, paratroopers, etc. (I think).
The pullup standard; 10kg x18+ seems to have been fairly regular, I believe Pavel also mentioned a 20/20 pistol test and a 50/50 24kg snatch standard with one hand switch.
In his book about the spetsnaz, Suvurov mentions a 3m broad jump test that seems to have been a 'minimum' standard much like the pullup test. Longer jumps, sometimes with body armor or a weighted pack, were done by many soldiers. 3m is a pretty high standard, Suvurov mentions how important leg training was for spetsnaz and says that they employed a variety of exercises--jumping for height or distance, running and jumping up and down stairs, running hills, and barbell squats for low and high reps.