"The AMM for the aircraft type will have limits on allowable play in the system."
But you just try getting these published limits out of your engineering department and see the result??!!
If the defect has been correctly deferred, then there will be a reference in the Techinical Log against which that deferral can be verified.
EG Play in flt controls within limits as laid down in AMM 27-blah-blah-blah blah. Repeat inspections to be carried out every xyz flt hours/days/cycles etc
Final action, to be repaired at xyz flt hours/days/cycles, A check,etc
If it's not deferred in accordance with any known documentation then a design deviation will need to be sought either from the airline/manufacturer's design office or NAA (or both).
Otherwise the engineer who signed it off in the log will be getting a visit from quality department.