In my experience compared to my panthers, my Parson's male actually is quite active and moves around the enclosure a lot. They are not as idle as one may think. I also notice that he loves to hunt aggressively. Could be a personal trait, but they are amazing hunters and will actively stalk a prey. Mine in particular will choose to chase down feeders and actually take a direct bite instead of shooting sometimes. I actually feed out of a large shallow bin (routine) and also will let some free in the enclosure occasionally (don't want strays).
More noticeably, they LOVE water and will bath and soak as much water as you can give them. While my panthers run away from water when they have had enough, my Parsons will bath and actually raise itself to catch the mist. It's an amazing thing to see.
In terms of challenges, I would have to say habitat size is a normal concern, and also maintaining the temps and high humidity. Because they love water and high humidity, problems can easily arise from mold and airborne infections. If your enclosure is small and doesn't allow proper aeration, problems will definitely arise. Large enclosures will aid in creating a great temperature and humidity gradient while allowing for better circulation and aeration.
As for being shy and easily stressed. I find that to be completely true. More so than other chameleon species I have, however they do gain the trust of the keeper. Over time I have seen him to be more calm and less afraid of me. I can pick him up occasionally with no physical signs of stress. But I seem to be the only person who can do this. He acts very differently towards my partner, again I am the sole keeper and interacts with him daily through feedings and cleaning. He is now at the point where he will feed directly from my hand (both shoots and also picks food up with his mouth).
One thing they do that I don't usually encounter in panthers is that they tend to want to "hide" before making a scene. When you reach in, most panthers will puff up and flash colors if they don't want to be bothered or picked up. In the case of Parson's, the first reaction is to tuck itself into a tight mass, and angle itself laterally with the branch showing as little surface as possible. They definitely fit the term "timid."
Just my personal observations.