Fixed many of these things, though the motor they drive is a lot bigger than the Dremel one, 250W, and the typical failure is the bridge rectifier diodes pop, and the triac blows short circuit. Replace the diodes with 1N5403 instead of the 1N4007, replace triac with BT156 ( because it is available locally and cheap), replace pot with another, because the originals are junky types with integral switch, which cooks, but is not needed as there is an external switch, and add a 275VAC MOV input and output. No noise filtering, but that is what you get with Chinese equipment, and no inrush limiter either, but at least the thing does have a 10A fuse in it.
Got in a few speed control boards off eBay, and added an external bridge rectifier to them, along with the MOV's, for some of the more prone to blow motors. Luckily there is a lot of room in the housing to fit them.