Oh gosh, I do hope you can get this repaired and the camera back into active service.
I've had this on my (now retired) EOS 5 in 1999 again in 2002. This dial on the EOS 5/A2/A2e is a terrible tantrum-starter. The trouble is the click stops on a pawl (that look like pronts on a fan bent up at the tips)) that are the mode selectors mesh with plastic slots, and it is very easy (way too easy) to strip the plastic slots out, even with normal wear, thus the free-spinning dial syndrome. Years ago Canon copped a lot of flak for this poor design and it has never been repatriated with something more reliable. Fortunately it's a cheap and fast repair, but a design weakness means it will happen repeatedly if the dial is subject to force e.g. trying to rotate it without pushing the central button down.
