These directories have to be writeable by web server (for me, apache). Set blogs.dir and ALL subdirectories to that user and group (for me, that's user and group "nobody"). Then set the priviledges to 755 for directories and 644 for files. 777 is just asking for trouble, I caused some for me.
That worked for my install.
If you are on shared hosting, tell support to,
"Change blogs.dir and all subdirs and files to web server user and group."
These lines will change the permissions of all the files and directories to the right thing.
"# cd /wordpres_directory/wp-content
# chmod nobody:nobody -R blogs.dir
# find blogs.dir -type f -print -exec chmod 644 {} \;
# find blogs.dir -type d -print -exec chmod 755 {} \;"
It helped to just give my host the commands for this.
See if it helps.
I had to ask them to change the owner and group of blogs.dir again, for whatever reason.
Good luck