I recently purchased an older home (built in the 50's) and had a 200 Amp Panel installed with a Sub-Panel of 60 Amps to the garage. I am experiencing some lights that dim when the furnance, A/C unit, or power tools in the garage are turned on. Is their any reason why the lights would dim, especially when the furnace, A/C unit and the garage are all suplied by their own electrical circuits and breakers?

Just a guess but did you have your supply lines( pole to house ) replaced with a larger guage to handle the extra load. Your electric supplier can guide you with this.
Mel W

In addition to Mel's reply, You might have your neutral connections (in your breaker box) checked to make sure that they are all tight. Make sure you turn the power off before you get into the breaker box.