Scott,

You should have no play in your tiller , that is a bad thing and will get worse .With a loose tiller to rudder connection , the tiller can be still and the rudder is moving back and forth creating more wear in the tiller head and heading for a failure.

A little play in the top of the rudder shaft ( due to missing or worn out bearings/bushings )is a completely different animal and can be tolerated but should be corrected as it negates the 'feel' of the boat while sailing , like a car with a front end that shimmies and is out of alignment .
You can get used to this slop in the steering and think it doesn't make any differance , just like you get used to a car with a bad front end , you can get used to quirks in the setup of a boat .