I have similar problems to socialsity:
* Widgets are not performing the functions that they should be. (This includes the tag function and adding a category.) What happens instead is the url changes based on the widget function but no effect can be seen on the edit page. For example the "add category" function creates the following url: http://fightthecurare.wordpress.com/wp-admin/post.php?post=65&action=edit#category-add
* The Insert/Edit Link and add media functions are not interacting with the post. Unlike the first bullet point, where the only sign of activity is the change in URL, the appropriate pop ups occur for each function. However, once the correct information has been inserted, the function redirects me to the last page I viewed in the edit link case or to a blank white screen in the case of the add media to post function.
* The edit post name function (which would normally change the url that a post would be available from) does not work. Like the first problem, the only discernable action is a change in URL.
I have cleared my cache and cookies in both browsers that I used (Firefox and Chrome). I have also asked my co-admin to attempt to use several of these features (I believe she used Firefox). I use wireless internet/DSL to connect to the internet (assuming either of those answers will provide the "how you connect to the internet" answer referred to in the OP).
I have not noticed any issues with menus on the dashboard.
I do not have access to edit the CSS for my blog's theme.
I should also note that the only aspect of the Insert/edit link function that is broken is the script that interacts with the visual editor. If I use html in the text editor, I can do everything that the insert/edit link function would do. The following work-around might help those of you who have the similar issues noted above and wish to add links: <a title="your title" href="www.yourlink.net">your text</a>