Yes, replace the receptacle with a new one, they're cheap and easy to do. Make sure you wrap the wires around the screws on the sides and don't use the small holes in the back that hold the wires in via a spring clip. These backstabbed holes are the causes of lots of loose connections.
The GFCI receptacles use back wired holes and actually hold the wires in via a screw clamp so they are good to use and different than backstabbed holes.
You may have a waterproof box mounted on the outside of the wall, if so make sure you install caulk along the seam between the box and the house. If the box is inset in the wall then no caulk will be necessary.
Either way you also need to install a while in use cover on the outside receptacle. This cover keeps any water from entering the receptacle and will keep your connections from rusting. Here's a link that'll show you about them. They're sold at Home Depot and most hardware stores.
http://www.leviton.com/sections/prod...ts/s5c12p7.htm
You should have a waterproof box mounted on the outside of the wall
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