The sixth season opener of Cold Case takes place in November of 1973. The Bachman-Turner Overdrive song "Takin' Care Of Business" is being played. That song did not chart until mid 1974. It doesn't take much research to find this out and should have been caught.
You can't go by when a song "charts". Songs can be accessible before that. A person can buy an album and listen to a song from that album and it may end up hitting the charts weeks or even months later. However, all is not lost with your argument. You still have a case it appears. Although I'm not familiar with the show you are speaking of, I will tell you that Takin' Care of Business was recorded in 1973, but wasn't released until December of that year.