Ac does not cool at slow speeds or at idle - 2005 Mercury Montego

The AC system requires horsepower so it may cause a jerk if the following is present, the idle speed control system is fouled up with gunk and slow to respond to the load change. I suggest you clean the idle speed control valve and the throttle valve with spray throttle valve cleaner and see if that helps.

Putting on the AC causes power to be taken from the engine, and that is quite usual (unless it's taking excessive power but if there are no noises and it's working ok that's unlikely).
That will slow down the engine (similar to switching on your heated rear window whilst idling)
What you are seeing is the idle is probably a bit slow, and it's too slow with AC on. Have a diagnostic run to check idle speed and mixture at low revs.

CHECK IDLE SPEED SHOULD BE 650 - 850 RPM. IF IDLE TOO LOW AC WILL PUT DRAG SLOW DOWN ENGINE CAUSING ENGINE TO STALL IF IDLE SPEED IS TOO LOW.

You might be low on freon if not compressor going bad to see if your compressor is going on and off turn on a/c on max have some one hold gas peddle down around 1500 rpm or just at a small fast idleif compressor goes on and off recharge it most likely one or two cans will be enough

Yes your "clutch fan" needs to be replaced. (Clutch mounted on your fan that attaches to waterpump)

if the AC isnt cooling on idle then the fan isnt coming on ,so gas isnt cooling in the rad in front of the car ,now as for the pulling away bit i wiould disconnect the servo vacumn feed pipe and block the end of the pipe and try that in case the diaphragm is letting in air causing the idle to speed up

Presurize system with radiator cap on to see if you are holding 10 to 13 LB pressure as high as 17 LB. Get new radiator cap for your radiator. Check for a slow leak at pump hose thermostat conection , is it wet ?
Do you have a Summer Thermostat ?
Vitally

fix the idle speed to 850-900 rpm
check the alternator and voltage regulator as the voltage should read 14.5-14.8 volts dc at 1000rpm or higher regardless of what is running
have it bench tested by an accredited auto electrician

defective ac compressor,that would be my guess

Your freon level is low, and not circulating on slow compressor speeds. Stop by any shop that has a sign stating they work on a/c and they can recharge it for you in a few minutes. Here where I live they charge about $20.00 labor plus a charge for the freon they put in, they sell it by the pound.