The flaps have long been a bit of a weak point in the system for the CRJ. Originally designed for the Challengers, the 100/200 flaps just didn't stand up to the reality of short haul airline ops. Numerous fixes have been made, as well as speed restrictions, and thus the new ones are much less prone to failures.
They are electrically driven, but the problems have come from a variety of sources such as a tendency to twist, and a complex drive system that uses two power drive units, to run a flex shaft which powers the actuators. Just about any little thing out of tolerance and "bing" you get a flaps fail message, and the flaps disable themselves.
The biggest cause of a lot of the problems has been the culture in some airlines of using the flaps as a form of drag control. Comair in particular is known for flying max speeds as long as possible and then dumping flaps at absolute maximum speeds as a way to slow down at the last second. Many pilots either don't notice that they are doing it, don't care, or are completely oblivious to the fact that such hard use (while still within the airframe limits) is needlessly causing things to burn out. For them, the result is an average of about one per day on their fleet of 120 odd airframes. Companies that baby things a bit have much less problems.
As far as landing goes, full flap Vref is in the 130-140kt range depending on weight (give or take a bit) and that gives 2700 to 2900 foot actual landing distance near sea level. Zero flaps has a 30kt correction factor to the full flap speed (160-170kts) and a landing distance 1.65 to 1.70 times the full flap distance (meatball numbers 3600 to 4000 feet). This makes for a very fast approach, and one that can easily eat up a pile of runway, consequently pilots tend to be a bit nervous about doing it!
As an aside, the 700 and 900 series have a different system, as well as leading edge devices which have the combined effect of virtually eliminating the flap problems, while at the same time ensuring at least some form of flaps available in the event that a failure actually does happen.