Safe rigging is essential for any aerialist to learn. You cannot be sure you are safe if you leave your safety up to others to check out - it is your life, after all!
I'm working on this page, so bear with me as I add more information.
Make sure that any fabric, slings, carabiners, and other equipment is up to climbing-grade or higher standards for load bearing. In other words, make sure the load ratings, usually marked in kN (kiloNewtons), are sufficient to hold the aerialist(s) when taking a maximum-height freefall from the very top of the apparatus, and add some more load on for safety.
Equipment such as slings and carabiners also have different load ratings depending on which configuration they are used in. Loading from the sides can be different than loading from the top and bottom. Make sure you completely understand this for your equipment before you rig.
If in doubt, talk with qualified individuals - climbing shops are helpful if you can't find any local help from aerialists.
It is UP TO YOU to stay safe. Inspect others' rigging before you use it. No one should ever be insulted by your inspection, or hurry you along into using equipment before you're comfortable. It's just responsible to ask questions and understand what you're getting into before you do anything on equipment.