The mesh can be used for the walls, windows, vents, and doors, and should be attached to the wood framing with washers and screws, or heavy-duty fencing staples.
If your coop is attached to an enclosed run, cover the floor of the run with hardware cloth, bring it up the sides a few inches, and attach it to the frame.
Simple bird netting or even a more elaborate pergola-style roof will prevent aerial attacks and keep birds of prey (as well as wild birds that may spread disease) out of the run.
Strive to build your chicken coop as solidly as you would your own house, and install an electric fence or electric wire around your coop and run.
On the exterior, I have gate latches and slide bolts on all of my doors and further secure them with carabiners (especially on the upper locks, which are more out of reach of critters).