Checking the evaporator and condenser coils to see that they are unobstructed, clean, and able to absorb/release heat.
Check on the refrigerant level to make sure that it hasn’t dropped. A loss of refrigerant charge usually means a leak in the system that needs to be sealed.
Check on all the electric connections and tighten them where necessary.
Clean the condensate pan and drain so the moisture from the evaporator coils won’t overflow.
Clean and lubricate the motors for the fans and the compressor to avoid mechanical stress that may lead to them burning out.
See if the thermostat is correctly reading the temperature and recalibrate if it isn’t.
Replace or clean the air filter. You will be responsible for this job during the rest of the summer, and you should do it once a month.