I've got a 68 single speed wiper motor that seems to struggle to wipe the windscreen successfully all the time. Got caught in some rain a few weeks ago for the first time in a mini and they worked ok. Today was out in the car today and they seemed to struggle and sometimes not work. The windscreen was fairly wet. When on they would wipe but on return they would be really slow coming back. Other times they would stop a 1/4 of the way up the screen and need a hand assistance. The rain was moderate. When I hold the arms up off the screen the seem to work ok

Lots of things happen with mini wipers.

Firstly the motor might just be tired. Might need rebuild (Convertable mini's job) or a new one.
The gearbox might be dry and sticky. Take the cover off and check.
The rack tubes could be dry, worn excessively or loose in the pivots. This requires dismantling, but not a hard job
The pipe could be loose on motor nut or the nut loose in motor. Watch it while wipers are working, check for excessive
free play in joints.
The contacts in self park switch might be worn out, or main switch might be poor. This'll cause low voltage to motor.
The wiper pivots might be partially seized.

That should keep you busy.