The problem is that ST2 doesn't update the theme automatically. So when Package Control updated the Soda theme, some of the image files got swapped, which confuses ST2. Restarting st2 should fix this.
Ah ha! I finally found it. Somehow I ended up with a `Soda Dark.sublime-theme` file in my `Color Scheme - Default` folder. When I removed that and restarted ST2, everything is displaying like it should!