Do gears mess up your odometer?

Yes, if you change out both the internal gear (inside the tail housing) and the speedo gear accessible from outside the tail housing then your odometer will be correct.

Side note: supposedly the 23 tooth gear used to correct the speedo for 3.55 and 3.73 gears will only last approximately 20,000 miles. Read this from a few different threads. Don't know what fails though. I would think that shops like Steeda and Brothers Performance would not sell the 23 tooth gear if it is known to fail in such a short amount of mileage. Guess I will let you know in about 15,000 miles.
 
Mine with 3.73 is way off, I had 2.73 stock and now at 60-65 I am showing 90-95 on my speedo. I once put over 100miles on my odo, with a 36 mile round trip. My odo. is now all frucked up and the speedo is now even starting to go (I think its from seeing 90-100mph all the time on the hwy) and it will just stay at 100 now if I am going 30-70mph and sometimes even when I am stoped it still reads 100mph.