Predators- cats, raccoons, possums, birds...many more here in SoCal. if you're going with 3/8" mesh or larger, I would suggest double walling your enclosure(but that's just me.)
Climate- make sure there is a cooler/well shaded zone for really hot days.
Poisonous bugs- I had to quit using my outside cage for a couple of months when I found it infested with ants and aphids followed by ladybugs(ladybugs are toxic, and ants can swarm and kill a chameleon). I've also caught my chameleon with a pair of black widow legs hanging out of his mouth. That was a nervous couple of days....guess it comes down to who gets/sees who first (not a gamble I'm really comfortable with, but it's just a fact of life here). I've seen video of a wild chameleon eating bees, so not sure how big of a problem that is. Wasps may be a different story. There are other toxic bugs too, not sure what they all are.
all in all, my best advice would be:
1. use 1/8" or 1/4" mesh screen/hardware cloth.
2. set up your plants and climate-zones throughout the enclosure thoughtfully
3. be conscious of your plant selection (ex.- Hibiscus is a great plant, but will attract aphids, which will in turn attract ants and ladybugs)
4. Pay attention to what kind of insects are in/near the enclosure. watch for webs, anthills...etc. remove anything you're not sure about
5. don't forget to close the door.