H2AD needed 100 octane, among other things. That started in 77 with the N model. 68 to 76 had the 150ph Lyc. Look....we are doing 172 trivia....
The H2AD did indeed have the infamous dual mag, but that in and of itself is not a show stopper. Lots of Lycs used versions of them, including the O360s in the 177B, and the O-540 in the Piper Dakota, and they have proven to be pretty darn reliable (once they worked out the kinks). The failure mode (the drive gear failing) that some suggest doesn't seem to have a huge impact in the operation of those engines.
The real show stopper for the H2AD was the switch to "automotive style" lifters. They came apart readily, especially in cold weather, trashed the cam, and showered the oil system with metal bits, with all the happy fun that usually entails. There were also issues with the external oil pump.
That said, with the proper application of service bulletins, mods and the infamous Lycoming "snake oil" lubricant (which most oils now incorporate), H2ADs can be darn reliable engines.
To the OP: You shouldn't have been flying 10-12 airplanes. You should have had it boiled down to 1 or 2 prepping for your ride (the 172 and whatever you were going to demo your complex competency in). The CFI is a tough ride...it requires signficiant focus on the material at hand.
Just out of curiosity....what was your mechanical background before you started flying? Not that it's required, but did you have any "techie" type hobbies? Cars? RC Planes (NOT the ARF variety)? Rockets? Electronics? Ham Radio?
The reason I ask is that kids these days don't seem to have a good grasp of basic mechanics or electronics. Ask one to change the oil in their car, and they drive it to Jiffy Lube. G1000s aside, most GA airplanes are pretty old school mechanically, and it helps to have a basic grasp on what's going on with simple IC engines.
Lots (if not the majority) of people have busted their CFI ride. It's not a show stopper. But I think your DE was correct, but expressed in the wrong terms. You need to change your "big bubble" approach and realize that these airplanes are not your dad's Toyota, where you hop in, press the button, and go 100,000 miles between scheduled service stops. That O-320 has more in common with a lawnmower than a modern auto engine.
Richman