REAR DERAILLEUR AND HANGER
The rear derailleur is a point of the bike that can see a lot of smacks on rocks. You want to give the derailleur a quick visual inspection and a quick wiggle to see how it’s doing.
First, look at the derailleur from the back. Confirm that the derailleur cage (the part that holds the two pulley wheels) does not have any bends in it. If it does, the derailleur will not shift properly and should be replaced. Also take a quick look at the derailleur hanger (the part of the frame that the derailleur bolts to) and make sure it does not have any kinks in it. Derailleur hangers are typically replaceable, and cheap and easy to do so, but its nice to know going in if this is required.
Now look at the side of the derailleur for any sign of rock hits or damage. A derailleur can be smacked on rocks repeatedly with no issues mechanically, but typically, the more often a bike has been ridden aggressively enough through rocks for them to hit the derailleur, the more likely other stuff is getting smacked on rocks, too.
Next grab the derailleur with your fingers and wiggle it from side to side. Is there any play, or does the derailleur feel nice and tight? This is somewhat subjective, but if you can feel play in the pivots of the derailleur itself, something is wrong.
Now grab the knuckle of the derailleur (where the cage attaches to the body of the derailleur) and press backward on the derailleur toward the rear of the bike. You want to confirm that the derailleur main spring has firm tension and returns quickly without slapping around.
All of these parts are fairly easy to repair or replace, but can easily add up to a hefty repair bill should most of these items require attention.
Part and Labor Estimates:
Rear Derailleur: $80-$150
Derailleur Hanger: $25-$50
Hanger Alignment (labor)- $15-30
Rear Derailleur Replacement (labor)- $20-$40 plus parts (cables, housing, etc.)