One thing sticks out in particular as not REST-ful: the use of a GET request for logging out.

(from http://en.wikipedia.org/wiki/Hypertext_Transfer_Protocol#Safe_methods)

Some methods (for example, HEAD, GET, OPTIONS and TRACE) are defined as safe, which means they are intended only for information retrieval and should not change the state of the server. In other words, they should not have side effects, beyond relatively harmless effects such as logging, caching, the serving of banner advertisements or incrementing a web counter. […]

[… H]andling [of GET requests] by the server is not technically limited in any way. Therefore, careless or deliberate programming can cause non-trivial changes on the server. This is discouraged, because it can cause problems for Web caching, search engines and other automated agents […]

As for logging out and redirecting, you could have a post to your logout URI give a 303 response redirecting to the post-logout page.

http://en.wikipedia.org/wiki/Post/Redirect/Get

http://en.wikipedia.org/wiki/HTTP_303

Edit to address URL design concerns:

“How do I design my resources?” is an important question to me; “how do I design my URLs?” is a consideration in two areas:

URLs that users will see should not be too ugly and meaningful if possible;
if you want cookies to be sent in requests to some resource but not others, you’ll want to structure your paths and cookie paths.

If JRandomUser wants to look at his own profile and you want the URL to be prettier than foo.com/user/JRandomUser or foo.com/user/(JRandom's numeric user id here), you could make a separate URL just for a user to look at their own information:

GET foo.com/profile /*examines cookies to figure out who 
                     * is logged in (SomeUser) and then 
                     * displays the same response as a
                     * GET to foo.com/users/SomeUser.
                     */

I would claim ignorance much more readily than wisdom on this subject, but here are a few resource design considerations:

1. Consumer: which resources are meant to be viewed directly in a browser, loaded via XHR, or accessed by some other kind of client?
2. Access / identity: does the response depend on cookies or referrers?