Hello ,
I have two me Supers and yes they do have a mechanical speed = 125. This speed is specifically to allow the camera to be used if the batteries have failed.
One of my Me Supers has developed a fault which manifests itself thus: if I turn the camera on ( by moving the switch from 'lock' to any other setting e.g. 'auto', 'manual', x125, or 'b' ) the first cocking of the lever will wind on the film but will not allow the shutter to fire. After this the camera will work perfectly until there is a delay of more than a few hours, at which point the next 'wind on' will be wasted due to the shutter not firing and the whole cycle repeats itself. I have not solved this issue yet and it may be what you are experiencing; I have heard it said that this is a known fault but no solution has been suggested. This particular camera has been used constantly for nearly 25 years without CLA so I can't complain.
Regards Daniel