It bugs me when FOs do something traditionally done by the Captain without asking. Or when the FO does something to set the tone without considering the tone I may want to set. For example:

The other day I was flying an all nighter from ANC to SEA. Almost immediately after take off the FO reached up and turned on all the overhead lighting. I was going to turn it on but not just yet. I like to wait until above 10,000 and clear of clouds etc...

Sometimes an FO will reach up and turn off the ignition when running the FL 180 check without asking.

I was busy on the radio, on two channels so the FO selected his own flaps.

While taxing out for TO the tower asked us if we could accept an intersection take off. He answer that we could without even looking at me or waiting for any indication from me.

The list goes on. Now don't get me wrong. I don't freak out yell at the FOs or even mention it. You asked what annoys me. There is a big difference between a little annoyance and a big problem.