For all the other arbors it doesn't matter if there's a little play allowing them to move back and forth by a tiny amount between the front and back plates as the wheels will still engage with the pinions. But not for the contrate wheel as this would alter the depth of engagement with the pinion on the escapement platform.

Replace the small brass piece covering the contrate wheel pivot hole. Adjust the screw over the pivot hole by the tiniest amount, first of all anticlockwise, until there is the least perceptible play. Check that the contrate wheel still turns completely freely.

You can wind the main spring by a minimal amount to check that the contrate wheel turns freely. Unwind it once you are satisfied.

Also, replace the ratchet (make sure it's the right way up) and its retaining brass piece, engaging it with the ratchet spring.