"Look at your trees, really try and understand what species of tree you have. There are a lot of great resources online that can help you understand the physiology of each specific tree but also just look up, down and around and make sure there's no visible issues."
Issues with trees that you should look out for and could make them more vulnerable would include:
Any dead or decaying wood
Cracks in the tree
Mushrooms or tree rot
As Richardson mentioned, there are online resources that can assist you with checking your trees and knowing what type you have in your yard.
You can get more information from The Arizona Municipal Water Users Association here or The Arizona Community Tree Council here.
Experts recommend if you see any issues with your trees or have questions, contact a certified arborist to address and mitigate those issues. Dealing with the problem now can save you money in the long run, as a stronger tree will handle the monsoon storms better.