Free range can be great. It has many benefits in terms of improving the mental health, stress levels, and tameness of your cham. It also has MANY dangers. Just about every free range cham owner has at least one accident or horror story. Your cham will explore his entire environment. After he learns where everything is, he will mostly stay on his tree (if it is well designed). The ENTIRE room needs to be cham proofed
Here are a few things that come to mind...
Open topped containers (garbage cans, empty fish tanks) that the cham can get into but not out of.
Electrical cords look a lot like branches and your cham will climb them. Electrocution becomes a concern.
Escape. It only takes one well meaning roommate to open the wrong window, or leave the door open for a few minutes for your cham to take off. From personal experience, looking for a chameleon outdoors is NOT FUN. Check your screens. Push on them HARD. My only free range horror story is that I lost a cham through a defective window screen.
Other pets. As far as I am concerned cats and chams are an absolute no no. I have both and my chams are in my snake room where there are no cats allowed. With a dog you can control the situation. You should not avoid it as you have been. You don't want the first time your dog meets your cham to be the time you forget to close the door all the way. Introduce the dog to the cham while you are holding it carefully. Let him smell the cham. Reward him if he acts gently and calmly, and reprimand him harshly if he tries to take the lizard in his mouth or gets excited and wants to play. If your dog is very interested in the cham, a squirt gun, shock collar, ect, can be good tools to discourage them. If your dog knows "down, stay" you can do that while you supervise the cham roaming at first. Some dogs have too strong of a prey drive and these dogs just cant be trusted with a cham. Other dogs would never hurt a fly.
Injury caused by you. It is easy to take a step backwards, or move a box, or open a door, and seriously injure your cham. If you free range your cham, the first thing you need to do EVERY time you walk into the room is find the lizard, so you don't do something stupid. If you have floors, the door will just slide the cham across the floor. If you have carpet (which I wouldn't recomend due to poop issues) the door can hurt them. I would put a plastic mat (like the kind for a computer chair) to minimize the chance of this injury.
No matter how careful, your cham will find things that you didn't think of. You should be very nearby for the first several days of free range.