Do you really have fuel vents on both sides? Most 172s have just one, and a vented cap on the other. There is also no stall horn or pitot tube on the right wing.
You need a circuit breaker check before start, and it's conventional to do a passenger briefing then as well.
Check the primer is locked at some point before run-up.
Before taxi, radio goes to ground, CD or CTAF. Not Tower. After (or before) run-up, it goes to Tower or CTAF. Ground only if you reject the run-up.
Transponder should be checked right after engine start, and set to 1200 or assigned code, on ALT. Until a few years ago, that was STBY. Just leave on ALT all the time per AIM.
Maneuvering, you should record altitude, speed and heading. You're going to want those numbers after the maneuver. You should also make at least two 90 deg normal turns for clearing. Lift a wing before every turn to check a really nasty blind spot.
I don't think your V-speeds are right for a go-around. Vx in particular should be the 20 deg flap value, not the flaps-up value.
After landing, it's a good idea (though not rigorously necessary) to trim for takeoff.
Fuel selector goes to left or right, not off, on shutdown. It only goes off if you're combating an engine fire or forced landing. Getting a gascolator sample when the fuel valve is off can be "interesting."
For securing, when the tow bar comes out of the back, keys are IN HAND. Period, no exceptions. Same deal for reaching through the prop arc for any reason. Never power over a tiedown.
You'll find the list of local frequencies will never be enough, and the ones that are on there you'll memorize very quickly. That's better kept elsewhere.
Emergencies should match the POH rather closely. Having said that, I don't understand why you would want to mess with ignition or fuel selector if the engine quits on the takeoff roll. Unless you operate on a very short runway where you'll overrun. Also, I'd leave the flaps down if they weren't already up for the extra drag.
The best way to troubleshoot a homemade checklist is to use it. You'll quickly figure out what's in order and what's missing.