I can see that the rear wheel is not centered between the chain stays. Is there an easy way to determine if the problem is with the dish of my rear wheel or are my dropouts misaligned?
...j
Wheel or just the tyre?
Check dishing: remove rear derailleur (only where it is bolted to the frame, leave chain and cable in place) and turn wheel around.
Or build a cardboard dishing gauge. Shape is like this:
__/^^^^\__
Feet should be wide and high enough to clear axle and most of the spokes, mine is about 40cm between feet and 12cm high. Remove wheel and tyre. Use a ruler / spoke / pencil as a "feeler": put gauge against rim and move the feeler such that it touches the axle lock nut. Keep feeler in place, turn wheel around and check other side.
Flipping the wheel around is a good idea--I'll give that a try. 40cm sounds too narrow for a dishing gauge. How do you use it?
The overall length is 70cm, the distance between the legs is 40 cm to accommodate spokes and hub. Place feet on rim, put feeler in place (should touch locknut) and keep holding it. Then: put feet on other side of rim and compare feeler position. If it is off by more than 1 mm you should redish the wheel.
Just turn the wheel and fit it the other way round.
If the centering also moves then it's the wheel dish.
If the wheel still centers as before then it's the frame / stays.
See Sheldon Brown for frame checking suggestion (string method).
http://www.sheldonbrown.com/frame-spacing.html
Scroll down to "Checking Alignment".
Besides the dishing, check that you haven't got too many spacers on one side of the axle, which is offsetting the hub.
Ride hard or ride home alone!