Diagnosis
Dust and debris build up on the ceramic heating elements and the fan intake, which reduces efficiency, can cause smells, and is a fire hazard. You don't need to fully 'get inside' the electronics to do essential cleaning.
How to Fix It
1) Unplug the heater and let it cool completely. 2) Use a vacuum cleaner with a brush attachment on the low suction setting. Vacuum all the exterior vents, especially the large intake grille at the bottom rear and the output grille at the top. 3) For the internal ceramic elements, look through the output grille at the top. You can use a can of compressed air (like for keyboards) to blow dust off the ceramic plates and the fan blades. Hold the heater over a trash can or outside while you do this. 4) Wipe down the exterior with a dry or slightly damp cloth.
If That Didn't Work
If you're still getting a musty or burning dust smell after cleaning, the dust might be packed in deeper. The casing is not designed for easy user disassembly. Forcing it open can break plastic tabs and is dangerous. At this point, it's safer to use it in a well-ventilated area for a few cycles to 'burn off' any remaining dust, or consider professional servicing if the smell persists.
Heads Up
Never, ever use liquids, sprays, or a wet cloth to clean the interior grilles or while the unit is plugged in. You're dealing with electricity and a heating element. Water can cause a short circuit or electrical shock. Dry methods only.