It seems that cold water or softened water are very poor at removing all the body oils and food stains from fabrics. This causes very thin (invisible) layers to accumulate over time. But not enough to see the residue. This provides an organic surface for the contaminated detergent to attach to. Just like it attaches to the plumbing in a washer.
This is a food source for the nasties and creates the Mystery Spots and odors. The spots are probably mold or mildew that grow enough on the fabric in the short time the garment is in the dryer to cause the stain.
Add to that: Cold water / soft water are not good at rinsing out the detergent and fabric softener so they stick to the oils on the fabric and it makes things worse than normal. Just think of what it is like rinsing shampoo from your hair with cold water or soft water. It takes a while. And, the machine timer / sensor does not know that. It can stop the rinse cycle before all the stuff has been removed from the fibers.
Add to that: Most people use way too much detergent so there is a lot to rinse away.
Put it all together and its a plausible scenario. This scenario is an educated guess based on the info available. But the solution given below seems to have worked for a lot of people. So, I’ll bet I’m close to being right...
This problem is an indication that you have biofilm growing inside your machine.
Run a Super Shock or two to blast it. Then use TechnoFresh to keep it under control.