The [http://www.repairfaq.org/REPAIR/F_SNES.html#SNES_006|sci.electronics.repair FAQ] has an entry on the SNES controller protocol, and it looks like the R button is the last button shifted out, out of 12 valid buttons. Is this what you read about clock cycles, or did you see something else?
It sounds like it could be some sort of timing problem or a flakey chip in the controller; do you have any other controllers to test?