The fonts look different in each screenshot, I guess is a CSS difference. Same CSS rules can be applied differently by different browsers, and if the CSS rules are edge implementations, it can differ from browser versions.
"Messages" denoted by a red, rounded rectangle vs. a red circle. There are a lot of reasons whay things might appear different.
For instance, something was changed by oDesk, yet your browser is pulling an older version from your browser's local cache.
Or, more likely, different versions are beiing sent to your broser from different locations. One version from the real site vs. other versions on third-party servers operated by oDesk's CND provider.
I think oDesk uses CloudFlare. I see reference to CloudFlare on the not found error page when the core site cannot be found, and the CDN is not working either.
For an article about CDN, see "Content delivery network" http://en.wikipedia.org/wiki/Content_delivery_network
If this particular instance is due to CDN or similar technologies, I would not say it is important enough to deal with. It could also be how each CDN server hosting the actual site (or portions of the site) renders the code for certain objects e.g., like the red, rounded rectangle vs. the red circle.
Now, if we were to start seeing differences in content, say a TOS with conflicting policies, then, that would be a real problem. I have not yet seen problems of that nature.
What does concern me on occasion is when the actual core site home page is not returned in the browser, and an error page results (the one that mentions CloudFlare). I would expect to see a copy of the home page from the CDN service.
Keep in mind that my posts in this thread are only my assumptions. I do not know for certain what caused the differece e.g., red, rounded rectangle vs. red circle. The next time I see differences, I will check to see exactly where the page in my browser originates from. That is, from the actual core site or another server.