you can change or delete the background picture, add a storyboard(and maybe a video as well? not sure), but pretty much everything in the .osu files themselves apart from editor-specific info(snap divisor, timeline zoom, etc.) can not be changed on your side only without needing to update it to the online version.
edit: ninja
winber1 wrote:
any way you change a map without changing its ranked status will have absolutely no effect on the playability of the map itself
take note of the "custom storyboard" part. it can definitely be abused, but i'm not sure if anyone actually does it