the gun doesn't move enough. it looks like it's pinned there. try freeing the gun up slightly, make it look more natural. otherwise, not bad.
how does it look right-handed?
When you make more key frames within the given frame limit, it smoothens its self out. As for the Right handed, its just taking a mirror practically and theres your right handed. So instead of Left hand being the gun holder, its the right.Etc etc.