The tug crew also monitor the RTF so that they can hear the instructions given to the pilot, as a safety backup to ensure that the instructions passed to them by the crew are the same as those given by ATC.
At Gatwick, we have a series of 'standard' pushback manoeuvres, unique to each parking position, which the tug drivers have to know off by heart. This saves time on the radio for normal operations. However, sometimes these are varied by ATC, for instance if they want the aircraft to push far enough back to allow an inbound aircraft on to the same gate. Occasionally, visiting crews whose first language isn't English don't fully relay all this info to the tug crews; this is where the crew monitoring ATC comes in very handy.
You will also notice the ground staff holding up a pin attached to a length of red ribbon. This pin is inserted into the nosewheel steering mechanism to override the aircraft's steering system and allow the tug to turn the aircraft. Waving this pin at the crew indicates that they have control over the steering.
Pushback is actually quite a complex process and the ground crew not only carry out a comprehensive final walkround to ensure all hatches are secure and that nothing looks damaged or out of whack, but they also monitor engine start, to make sure that no-one is going to get blasted and that fuel doesn't start leaking out or whatever. Correct setting of brakes at all stages is another major issue and the ground crew are firmly in charge, here.
Being a part of the pushback crew is a highly responsible position and most of the folk I know who do this job take flight safety very seriously.
TheOddOne