I would defo change the filter if not done recently, ie in the last two years.
There should be ABSOLUTELY NO PLAY AT ALL, in the dizzy shaft, if there is, it has likely spun the top crushed iron bush, as these are crap, theyu pick up and spin in the alloy housing of the dizzy body, they can be repaired (£35) with an oilight bush, for perfect problem free running.
The arm should have no play, but a lot do, a thin piece of card inserted between the arm and shaft stops this.
tabetha