In the gif below, I applied a copy rotation constraint to the lower bone of the upper arm. It is copying the rotation of the larger bone directly on top of it. While the influence is set to 1.00, it works fine, but the moment I turn it down the entire bone flips to a completely different direction. I made sure it is copying the correct bone, and the rotation is set to local space.
It may be just a problem with the armature itself. In a separate file, I recreated the shoulder area with the same constraints, and it worked perfectly. The mesh does not get messed up when I add the copy rotation constraint or adjust the influence. If it works here, then what is causing the constraint to fail in my original file?