Interesting .. in his for sale ad he had stated "All stepper units have been cleaned and adjusted. "



I agree with Steevsee , problem 1 sounds like a Stepper issue .. problem 2 will be a ball count unit issue .. check that when it resets that the wipers are actually on the the first position . Ball count unit is usually found in the backbox.
A manual and schematic will really help you out with troubleshooting as will the labels on the steppers and relays , if they are still there.

Link to manual is here http://mirror2.ipdb.org/files/438/Bally_1976_Capt_Fantastic_FULL_Manual_United_States_Domestic_.pdf

Link to Schematic is here http://mirror2.ipdb.org/files/438/Bally_Capt_Fantastic_1062_Schematic.pdf

Good luck
Dave