The camera used for the take off from the moon shot could have been remote controlled too.
Actually, thats exactly what happened. The camara was part of the Lunar Rover-the land vehicle the astronauts used during the later landing missions (it was actually used on Apollo 15, 16, and 17-the final 3 missions of the program). The camara was generally used for surveying the aera's and giving mission contorl an idea of what the astronauts were doing and what they encountered. For example, it gave the lunar geology people back in Houston the ability to view what samples the astronauts were taking and allowed to point out anything specific if they wanted a special sample. This camara was remote operated by a man at one of the consoles at Mission Control in Houston, Texas.
Although not the primary use, this was the same camara which was used to film the assent of the lunar module when the astronauts left the moon. At the end of the 3 missions which had the rover, it was positioned a little way from the lunar lander so the liftoff could be viewed. So, there should be 3 different videos of this-well thats not the case (there is really one 1 that is commonly known-although I have seen all 3, you can find them online in various places).
The lunar module (LEM) liftoff of Apollo 15 could not be followed by the camara on the rover because the camara could not move up or down (only side to side). So, there is a video of the launch but you can't see any of the assent, the assent stage of the module quickly lifts off the screen. The rover used on Apollo 16 did have the ability to move up and down. But, you have to remember that there is a delay wend sending signals from the earth to the moon so the controller on earth would have to time everythign just right to view the launch. Unfortunately, the camaraman's timing for the Apollo 16 LEM launch was not that good, so you can see the launch but before the camara begins to move upward the module leaves view. So, Apollo 17 was the last chance and the situation was basically the same. The only difference is the man controlling the rover's camara from mission control (his name escapes me at the moment) timed it perfectly. So, the Apollo 17 LEM assent was filmed by a remote controlled camara on the lunar rover.