Maybe this will help someone in the future...
My Dad was complaining that his rather old Maytag electric dryer smelled like something was burning whenever he used it.
I pulled the front and top and turned it on. A short time after the heater coils came on, I noticed a burnt smell. I tried a no heat setting and there was no smell, so it didn't appear to be a belt or the motor or anything electrical.
I checked the air flow (really strong), I checked the exhaust hose & vent, etc. and everything was clear.
The one duct I was having trouble checking without taking the entire dryer apart was the flat duct in the back of the unit where the heat actually comes into the drum from the heater coil. There is a 3/4" hole at the top of this duct, but I couldn't shine a light down the hole and see into it at the same time. Shining a light from inside the dryer didn't light up lower half of the duct so I couldn't see the bottom.
Then I said to myself, "Self, the heater coil throws both heat and light. Maybe if I start the heater, it will light up the bottom of the duct enough that I can see if there's anything down there." Sure enough, as soon as the heater came on, I could see some burnt debris at the very bottom of the duct.
I turned off the dryer, found a long thin tube in my Dad's shop and taped it to the end of his vacuum cleaner hose. I stuck the tube into the hole at the top of the duct, fed it down to the bottom and heard the debris get sucked up.
When I turned the dryer back on, the smell was gone.
I don't know if it was bugs or paper or what (I didn't feel like sifting through the vacuum bag) but whatever it was was apparently burning just a little bit more each time the dryer was turned on.