You need to make sure that the building stays safe. You need to make sure it's up to code, that the wiring is fine, that the sidewalks are even, and any stair railings are securely fastened. If your complex has a pool, you need to worry about those who may be swimming, about hiring a lifeguard if your township requires it, about keeping the water clean, and about dealing with any "accidents" kids may have quickly. It can get exhausting and if you focus on worrying about all of this, it can drive you slowly insane. Unfortunately, the list never seems to get smaller but really that's a good place to start.
Make a list of things you need to keep an eye on. Start with the obvious things, like the sidewalks, railings, parking lots, etc. As you think of things, add them in. How are the lights around the complex? Do you have a laundry room, and if so is it clean, bright, and safe? Do you have a plan for winter with the snow and ice? Continue like this until you cannot think of any more. If you have a board for your complex, maybe create a Google Doc so others can add their concerns as well. If you aren't living in the complex, it may be difficult for you to notice the little things that the residents do like a dead tree or a beehive that has started to develop in a back corner. You never know what may pop up, but having a couple of people who are observant help you can go a long way.
If you have a complex, you already have enough to worry about. Times like these are when Talley can help you the most. We take care of maintenance calls and many safety concerns. Focus on what you need to and leave the rest to us.