Great advice here! But watch out on the rust.
The detergent dispenser is an easy fix as Barcoboy described. Don't be surprised, though, if you break a screw or too. If the old dispenser leaked then some of the screws are likely to be rusted as well. If that happens, just go to Lowes or HD or Ace Hardware and get a similarly sized screws in stainless steel and install them on the new part. As mentioned before,turn the dispenser the opposite way the original was installed.That will prevent any future leaks from coming in contact with the wires that attach to the bi-metal heaters. You may have to extend them so, again, go to Ace and get the proper sized connectors and some butt connectors to splice in the new wires and you should be good to go.
NOTE: the wires marked DC1 are for the prewash door and DC2 are for the main wash door. It is best to connect them where they belong so the doors are loaded properly with detergent and will open at the right times.
Also, if you use the newer style white bi-metals, they can only be installed in one position since they have a locating hole that fits over a peg on the detergent door and that should be just about perfect a position to allow the doors to open up when called for.
As warned before.. TURN OFF THE POWER AT THE BREAKER!!! There is current(120v)sitting in those wires even when the machine is off so you can get a really nice jolt from them and NEVER, EVER, connect the bi metals to a full 120 volt power source as you will cause a direct short circuit. You cannot test them that way.
They work by running a load thru them, in one side and out the other to cause the bimetal to heat up and bend which then releases the door. On your machine, the pump motor is switched from the timer thru the bimetal when it is time to open the specific door and then switched back to a direct connection thru the timer to the motor. Same goes for the wash door. You won't notice any change in the sound of the motor at all, just the door opening. Later machines used the motor amperage draw for one door and sometimes used the heating element amp draw to open the other door. This actually provided more accurate activation of the door as the amp draw was always the same. The pump motor draw was dependent on the load put on the motor by the water in the machine.
As far as the rust is concerned, make sure you are not mistaking actual rusting and scaling of metal for simple rust staining due to water conditions and perhaps some foreign material that may have left a rusty residue in a particular spot.Determine what it is with your finger nail and not some hard scraping type of object. Once properly diagnosed, you can proceed from there with a repair if need be.
Hope this helps.