If you're using $wgWhitelistRead, make sure that the style sheets and .js pages are accessible.
I was then, I'm not now...
Another issue I noticed then but haven't checked since was that when $wgWhitelistRead was on, IE users got a script error on the front page if not logged in and didn't if logged in. I don't use Windows so I haven't checked since.
If not, could you provide some details of your configuration that might be different from the defaults?
Err, where to start...
My 1.3.5 was extensively modified, although not on any of the files 1.3.6 changed. I've got $wgWhitelistEdit (I think thats what its called) turned on, the copyright notice on the edit page hacked out, extra buttons added to the editbox, and a few other random hackjobs to make it work better in the enviroment I use it. But no major changed to config files.
Cian