I've done several of the above including:
flying most of the way to France in a Robin with takeoff flaps;
taking off on 08 at Old Sarum in a C152 with carb heat on (wondering why the hell we weren't reaching Vr in any kind of a hurry);
taking off in a PA28 with one fuel cap detached and sitting on the wing - it fell off during takeoff and was retrieved somewhat dented by a rather sarcastic ATC...
changing tanks in mid-flight in the same PA28 and turning the fuel selector to 'off' (one of those moments when time slowed down... I realised immediately what I'd done but still had time to plan my mayday call!)
Tim