There are a number of problems with this movie:

There are two real sources of noise that limits the radio astronomer's ability to search for very weak signals, the galactic halo noise and our atmosphere. The Galactic noise halo interferes with us below 1GHz and noise due to earth's atmosphere interferes with us above about 10GHz.

This pretty much keeps all SETI searches (at least radio ones) between 1 and 10GHz. Inside of these two frequencies, the noise drops even closer to the 2.7K cosmic microwave background between about 1.4 and 7GHz. This is why many of the SETI searches and much of our radio astronomy research is centered around the frequencies that the OH (hydroxyl) and H (hydrogen) molecule masers emit. This is the so-called water hole you may have read about (H - OH). Tell me scientists don't have a sense of humor. :-)

This is also why it would be assumed that any interstellar transmissions would be within the 1 to 7GHz frequencies as well.

Most large dish antennas, such as the one shown in the movie, are microwave receivers with very low noise front ends. As a previous poster pointed out, the first amplifier is the critical one with regards to noise. Not some silly box in an attic. Also these antennas have specific feeds that would not allow you to pick up an FM broadcast anyway.

On to the backyard dishes: The dish positioners on these antennas are designed to only sweep out the arc that the geosynchronous satellites are located on. They also have a feed/front end that is not designed to receive an FM broadcast in the MHz range. So unless he added an entirely new FM feed assembly, X/Y drive (or alt/az etc.), and control circuits that did not interfere with the normal operation of the dish from the home owner, it just would not work.

Also a dish antenna is not the best antenna for receiving an FM broadcast in the MHz range. He would have done better with a tuned yagi I think.

Lastly, if this race was so advanced in their technology, why would they not be using something like a microwave burst frequency hopping 8-ary encrypted signal.