Heaters use a lot of power and can easily exceed the capacity of an already loaded circuit. Anything with a motor or fan will use more power when starting up than after it is already running. If the circuit breaker or fuse is tripping when you plug in or turn on the heater, then you may have too many things on that circuit. Look at every electrical device on the circuit and add up the total watts of each one (it's listed somewhere on each, usually the back or bottom). Divide the total wattage by 120 to get the total amperage needed on that circuit. The fuse or circuit breaker should be rated for at least as many amps needed or it will trip when the total is exceeded. You may have to find another place to plug the heater in or have a circuit added to handle the extra load.
DON'T replace the fuse or circuit breaker with one rated for a higher load, the wiring may not be able to handle it and you could start a fire within the walls or attic. (Using extension cords for heaters in a house is a bad idea because the cord can overheat and start a fire.) If you aren't comfortable with this, find someone that knows what they are doing or hire a licensed electrician.
The switch to the appliance is down stream from where the power comes in from the plug. Even though the appliance is turned off at the switch the appliance has electricity up to the switch. As you stated there will be voltage potential right up until the pins of the appliance become disengaged from the receptacle If you have ever noticed a three blade plug, the ground pin is longer that the hot and neutral blades. What this accomplishes is that when plugging in a device the ground is made first and when un-plugging the ground is the last to be disconnected. By holding the appliance you were at the same ground potential as the appliance. By touching the "hot" side of the plug when pulling it out you became the return path for the electricity to flow. If you had touched the neutral side of the plug when pulling it out you would have felt nothing. Be careful when removing plugs from receptacles. Always pull on the plug body and never on the appliance's cord
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