I'm looking to install a thermostat that requires a "C" wire. See the picture below of the terminal inside the furnace one of the blue wires appears to go to the cable that goes outside to the compressor. The other blue wire goes to the thermostat wire for the thermostat and is not connected to the thermostat. Is there any issue using that C wire for a new thermostat that requires one? Any precautions for installation and instructions other than turning the power off to the furnace would be appreciated.
Go ahead and use it
The fact that there is a C wire going out to the air conditioning compressor is normal where air conditioning is installed. In fact, in systems with air conditioning where the C wire isn't clearly labeled, tracing the wires out to the compressor is a good way to find where to connect a C wire to.
So, go ahead and hook your blue C wire up to your new thermostat -- there is nothing else you need to do to have a functioning C wire.