I bought a home back in August and the previous owner had a new 3-ton HVAC system installed. Basically right now the HVAC is located in the upstairs hallway, and the way the duct is set up is there is a central return vent right underneath it (12x24) that pulls air directly into it and another return duct in the master bedroom (16x24). I have noticed that the main return vent under the unit makes a loud whistling sound when the unit is running. If I open the vent I can see that the air filter is bowing inward because the unit is sucking air in so hard it causes a lot of pressure. This does not seem normal. I am wondering if there is not sufficient return. It could just be that there is a lot more air being pulled in at the main vent because that is the closest opening (path of least resistance). The upstairs bedrooms often get very hot during the summertime and especially when the doors are closed, since the gap under the door is not very big and the inspector said that creates positive pressure that prevents air from coming out the supply vent in there. I am wondering if it would be wise to have a new vent installed in one of the upstairs bedrooms in order to alleviate these problems. I reckon I will have to have a certified A/C guy come out and give me some advice. I was hoping that I could find someone on here.
A whistling sound at the return often indicates the grill is too small relative to the duct attached to it.
Does consistently leaving the doors open allow the system to sufficiently heat and cool the home?
For most bedrooms with more than 100 cfm of supply aor a 1 inch door cut is not sufficient opening for return air. If you have carpet installed it is likely you have less than 1 inch. Transfer or jumper ducts may help alleviate the pressure the home inspector noted. This can be easily checked with a manometer. The pressure difference between the room and the central area where the return is located should be 3 pa. or less.
Experiment by leaving all the doors open (as much a possible) for several days first. If leaving the doors open and/or providing better return circulation does not resolve the issue, then other help is needed.
Based on your other it sounds like you need a competent HVAC tech to troubleshoot and balance your delivery system. It is also possible that you are undersized or there are some other issues (like excessive duct leakage, or set up issues) if you are having trouble maintaining the desired thermostat set point.