I've never found a mnemonic that works for me since there's way too much to check, but I have found that going in a specific order, each and every time, really cuts down on errors.
One of the things we always do is a "head to toe" equipment check, starting with hood/mask down to fins. Any differences in equipment are discussed en route.
So, for example, it'd be something like:
1. Hood
2. Mask - make sure there's suction, strap is not wrong.
3. Regulators - breathe primary and backup, confirm correct hose routing.
4. Wing inflation and deflation, test OPV
5. Drysuit inflation/deflation
6. Instruments and gloves (computer/timer, compass, camera etc.)
7. Lights and backup lights, strike to confirm batteries are good, hooked up
8. SPG
8. Harness buckles and straps
9. Knife
10. Weight belt, tail/v-weights
11. Pocket contents
12. gaiters/boots
13. Fins
Once in the water, we'll perform a quick bubble check on each other, flow check of tank valves and air-share donate to ensure regs are breathing correctly underwater and hoses are routed correctly. Then we go dive!