Nice save, Guy ! This is a more modern version of the Mobile Maid - the three-level wash system and lift up upper rack are great features.
About the detergent cup, I am not sure if these later models had a magnetic trip for the release or if they were tripped by a cam from the timer. Try slowly rotating the timer dial clockwise to simulate a full cycle - you may hear a snap in the main wash part of the cycle and if so, the cup is tripped by the timer. Bring the dial to off and try to rotate the cup up to see if it will stay in the 'up' position.
You'll probably want to take the front access panel off to investigate the rinse agent dispenser to see what may be causing the leak. Worst case here would be that the solenoid that opens and closes the dispenser is stuck in the open position.
I've used a shot of steam (yes, I know how crazy that sounds!) to free up stuck pushbuttons on a blender in the past. I used one of those hand-held steam cleaner machines and after a thorough drying period (48 hours) the buttons worked fine.
I think the part in the far right of the tub is a vent, but again it's been a long time since I got up close and personal with a Maid of this vintage (although that will be changing soon, I hope!!)
Congratulations on a neat find!!