While Idling the rpm jumps up and down

Here is the common cause of surges (idle speed goes up and down), stalls at stops, slow idle speed, erratic idle speed, rough idle and engine hesitation (and other problems), it is in most cases the idle speed control air-bypass valve and or throttle valve and upper intake, these area's get full of gunk and combustion residue over the miles and cause idle issues (stalls, low idle) like yours, Get a can of intake cleaner from any local parts store, not carb spray, intake cleaner, it is made by a company called CRC, remove the air intake hose to the engine, hold the idle high so the engine won't stall, then spray the can of cleaner into the intake while keeping the engine running, use at least 1/2 the can, shut down the engine and disconnect the battery for 5 minutes, then restart and complete a number of mixed driving cycles, town, freeway, stop and go etc., after a few days the problem will go away as the system will relearn to the clean intake.

If is very common on the Acura Legend to have air in the cooling system. This air in the system will cause the idle speed control valve to see changing temperatures. There are several procedures online for removing air from the cooling system.

I have to agree with Scorchingwar regarding the cooling system having air bubbles. This is a classic symptom of that.