The covers/doors on mine are quite stable, fortunately. As to the bottle, it is softer than the normal Reo bottle. Not as soft as the silicone ones, which I did not like.
Mine has the most annoying wobble... both the ones it came with and the leather ones I got as well. But @Ugi gave me a fix which I will try... he removes the screw bottom right and replaces it with a slightly bigger head and he say that fixes the issue.