Quoting the reaction enthalpy as positive because the temperature went up.
Why it's wrong: A rising thermometer describes the surroundings, not the system.
Check instead: Water warms means the reaction released heat, so the reaction q is negative.
Treating heat and temperature as the same quantity.
Why it's wrong: Temperature is intensive; heat depends on how much material there is.
Check instead: Ask whether the quantity would change if you doubled the sample.
Including the water as part of the system in a coffee-cup experiment.
Why it's wrong: The water is the measuring device, it is what absorbs the released heat.
Check instead: System equals the reacting species only.
Saying an endothermic reaction feels warm.
Why it's wrong: It draws heat out of its surroundings, including your hand.
Check instead: Endothermic feels cold to the touch.