There is an arm that is attached to a bracket on top of the differential. It attaches to a bracket on the left side of the chassis. When I was greasing the chassis today, I noticed that the side of the arm attached to the differential has a lot of play (forward and backward). Is this ok?

Thanks,
Rick

That sounds very much like a panhard rod, also known as a track bar. It is designed to prevent sideways movement of the chassis relative to the rear axle. Fore & aft play should be no problem, unless you see signs of damaged/deteriorated bushings.

Yep, it's the same as on mine, although mine is attached near the wheel.