It depends on just what's 'wiggling' around.
If the barrel assembly is indeed the loose part, then that's not normal nor is it a good thing. The barrel assembly needs to fit tight in two places: on the cylinder base pin (also called arbor or cylinder pin), held by the wedge through the slot in the barrel and the base pin, and on the two locating pins at the front of the frame below the barrel assembly. If there is a gap between the barrel assembly and the frame at those pins, and you can move the barrel assembly at that location, you have a problem that needs to be fixed.
On the other hand, if the looseness you are describing is cylinder end play, that is fore and aft movement of the cylinder (NOT the barrel assembly) on the pin then whether there is a problem depends on how much movement there is; a small amount is considered normal and acceptable.