My brother bought a Trek 2120, 1997 or 1998, that had been upgraded to a mix of 105, Ultegra, and Dura-Ace. Last week his chain skipped of the rear cogs and caused a crash. Upon further investigation we might have some capatability issues. Here are the components that are on the bike. I know an obvious problem right away is the 8 spd in the back and the 10 spd chain. Are there any others?

Crank: Dura Ace 7700
Chain: 10s
Cassette: 8 spd Hyperglide
FD: Ultegra 6600
RD: Ultegra 6500
Brifters: 8 spd 105SC STI