The use of checklist is of course, as the name suggests, to check that you have done everything as needed. But as DirectAnywhere said, there are just times when you can't refer to a checklist for whatever reason, that's when you need, what I call, a "Killers Item" checklist. For instance, a takeoff checklist would only contain: Flaps, Fuel Pump, Trim, Prop Pitch....and whatever is specific to your aircraft that, if not done, would certainly cause you headaches!
Personally, I do a flow pattern around the cockpit, then use the mnemonics on taxiing, and the killer items checklist just before takeoff.