I would flush the washer with a treatment of Affresh or one of the other approved cleaners for frontloaders to see if there may be residue from fabric softener, etc getting on the load. The MAH6500 was a machine that we built specifically for Home Depot, having the same features as the MAH5500 but with an internal water heater as well.
The dryer no doubt has some sort of a venting problem which has lead to the burning odor, and the dryer should be serviced by an experienced technician familiar with the Maytag drying cabinets. A vent problem with the dryer can also cause staining due to accumulated lint, vapors, etc. (No foil duct. no kinks in the line anywhere, etc). At the very least, the dryer will likely have to be disassembled to inspect it properly and clean the interior of the cabinet.
If you are real handy with a screwdriver and can follow technical directions well, here's the manual for the Dryer cabinet:Maytag Drying Cabinet Service
Affresh Washing Machine Cleaner Part # TJ120