EDIT: This is fixed. It should be safe to dive back in.
Chrome changed the way it accepted inputs to resize methods in v25, so we had to modify our resize code. They're not as forthcoming with release notes and regression testing as we are!
EDIT: This is officially logged as a known issue - Developer Console log viewer fails to display correctly on Chrome v25
EDIT: It appears this issue exists in Chrome 25, but not in Chrome 24.
UPDATE: There is a known incompatibility between EXT 4.1 and Chrome 25. When your browser got auto-updated, you got to experience this first-hand in the developer console. The layouts stop rendering, which is what you see (or don't see). Sencha, the creator of the EXT library, is working on this issue, and we're waiting on them.
What we found in doing a lot of repro work is that the workspace can get messed up by opening a log with three columns (stack tree, execution log, and source, for example). If you change the default perspective to exclude the stack tree and execution stack, you should avoid the rendering issues.
Firefox seems to work, so that's probably the easiest workaround while this general bug gets sorted between Sencha and Google. Another option is to uninstall Chrome 25, reinstall Chrome 24, and turn off automatic updates. That seems like overkill compared to using Firefox, but it should work!