I am having the same exact problem described here:http://community.office365.com/en-us/forums/164/p/18936/86397.aspx as well as in several other posts.
Basically when I select Change Picture from OWA, it brings me to my profile page but there is nothing on that page where I can actually change or edit anything. The Change Picture button is missing. I have tried resetting IE as well as adding the portal site to the safe sites list in IE. This happens on multiple computers both on and off corpnet and domain joined as well as non-domain joined. Something seems to be screwed up with my account.