the part you are asking about is the rotor button. and no it should not have excessive play. it may have at the most an 8th to 1/4 in movement. a new on costs about 8 bucks. but you may want to have your distributor gear and your timing chains checked. excessive play will lead to poor drivability
__________________ '87 gt ttop, 306 stroker, lunati custom cam, hardened pushrods and guide plates, ported and polished '69 hipo heads with 194i 160e, harland sharp gold rockers with triple valve springs, fed by 670 street avenger hooked to a offset torker 289 intake, fired by msd 6-al | 
1966 Mustang 200cid distributers 
