Hitec's Spectra 72MHz module was a great innovation, not unlike the variable frequency transmitters from Multiplex. This module did away with the need to change a crystal to fly different aircraft Unlike the multiplex system, however, there is no front-mounted user friendly dial. Instead, Hitec's Spectra Synth module featured two small dials and retuning required a 2mm flat head screw driver to turn the dials. This system have proved very reliable for me since 2005, but I began to get interference like symptoms two years back. There was never a case of loss of control, just ticking and twitching servos. As it turned out, I was not alone. The issue is caused by a high resistance connection between the transmitter and the Spectra where the 5 pins plug into the module. So if you have a problem with Hitec's Spectra or Futaba's Synth modules, check here first.
The 5-pin white connector, the source of your trouble is relatively simple. The connector is the female 5-pin Molex Connector, Digikey offers a replacement previously listed as Part# is WM3103-ND.
The RF amplifier stage is set on the outer-most end of the module and uses the surrounding aluminum shield as a heat sink. The Spectra becomes very warm after an hour or so, but this is normal.