How much exercise is too much?

First post, so I hope this is in the right forum. Our dear Max is 4 1/2 months old, and coming along just great. A friendly, loving, smart, gutsy dog (the 4th of July fireworks at the Rose Bowl didn't faze him at all!).

Wife and/or I walk him morning and evening--each time between 1 1/2 and 2 miles. Lots of other dogs, so he has a great time. But last evening, after a particularly long morning walk, he seemed to be limping. No sign of pain, but definitely favoring one leg. After his morning walk today he took a long, long nap, and when he woke up he again seemed stiff on one side--but the other side! Again, no sign of pain, and more than willing to run around.

So, are we walking him too much (easy fix, obviously), or is this normal post-exercise stiffness, just like humans get? Or should we be worried that there's some structural problem?

Any and all advice welcome. We're both veteran dog owners, but this is our first GSD.