The rear caliper is designed to slide from side to side on two pins. You can push and pull it back and forth by hand - is that what you mean by 'play'? If so it's perfectly normal. Instead of a 'floating disc' (as on the front brakes) you have a fixed rear disc and floating caliper.
If the caliper is rattling around front to back as well, the sliding pins could be worn.
There's a rubber boot over each sliding pin. Pull it gently out of the way and check that the pins are clean and lubed with copper grease. If these pins seize up, the rear brake will bind and the pads will wear unevenly. The pins are more likely to seize up than wear to an excessive clearance.
Hope this helps,
Ian.
