Is it permissible to attach more than one neutral or ground wire to any terminal screw on the service panel bus? A home inspector says this is not allowed. THAT DOESN'T SEEM RIGHT, because all of these wires are being bonded to earth ground - they are all the same point, electrically.
The issue isn’t about mixing ground and neutral on a single bus in the main panel. That is allowed although it’s preferred to have separate neutral and ground busses, both bonded to the chassis and grounded.
The issue is that most panel busses aren’t rated to have more than one wire per termination point. Some are but most aren’t. The issue, other than just the question of certification, is that they may just not be designed to hold two wires securely or to keep a tight connection over time.
If you can post a photo of your panel, or at least give the brand and model, someone here should be able to give you a specific answer.
This pivots on NEC 110.3(b): You must use equipment according to its labeling and instructions.
If the labeling/instructions say you can do it, then you can do it. For instance my Pushmatic panels have wire capture slots on both sides of each screw on the N-G bar, so it's no trouble at all. My CH panels do not have this.
If your bars are full, the best course is to add ground bar(s) as needed, and move grounds off the neutral bar to the new ground bar(s).
In a perfect world, you have 100% separation of neutrals and grounds, and a neutral-ground bond that is a fat wire positioned so you can get a clamp ammeter around it. (It should read 0A).
On Square D panels, back then and into now (there have been few changes to anything), you have always been able to put 2 x #14 or #12 on each hole in the ground / neutral bars, regardless of if it is G or N.
But as previously stated, you must follow the mfr instructions. There should be (would have been) a paper label on the inside of the door that would describe this. If that is missing, you are going to be hard pressed to find corroborating information from Square D as they are now owned by a French company that couldn't care less about old stuff, so getting someone to look up old data is all but impossible. However if that original label is there, it should be all you need. Remember, the cover was undoubtedly off when the inspector looked, but it's not his job to root around to find your cover, it's your job to point it out to him.
Side issue: Whether or not your Gs and Ns are mixed has only to do with whether or not this is your main service panel, i.e. the first place where your utility connections land. You CAN mix your grounds and neutrals in the service panel, you CANNOT mix them in any sub-panels.