The very first item is easiest to examine: drain system. This is important to make sure that any clogs in the HVAC system do not damage the equipment, or result in secondary harm. Make sure to look for drainage lines and draining pipes. An emergency float switch is an excellent idea. It will cut off the electric power supply to the machine once the level of water reaches a specified point in the draining pan.
Make sure you check the temperatures on both the return and supply sides of your HVAC unit to confirm the unit is working efficiently. It should be 18-20 degrees of difference between the two ends. You may need to address any leaks of freon that exceeds the level of the other side.
The final item on your list is to check that the HVAC system is able to adequately heat and cool the entire square footage of the house. The data tag should show how much the system can handle. You can add up to 500 square feet. For a better idea of whether there are any drafty spaces in your home, measure the size of the machine to the size of your dwelling.