I’m attaching a screenshot of what I see when I first go to the Forum Admin page after installing the forum on a site.
Notice the errors — and how the errors relate to folders that weren’t able to be created within the blogs.dir file structure (which no longer exists in the current WP version if I’m not mistaken).
What is the correct procedure to resolve these errors?
This is a multi-site install? I am no expert on MS but are you saying that ‘blogs_dir’ is no longer used?
As to correcting the paths then simply create the folders needed and set the paths to them in the form above. The popup help will tell you more if you need it.
correct.. sort of… 
new multisite by default does not use blogs.dir… but any existing multisite that had it still uses it… and in quick testing with new install, there is no issue if it gets created and used… its just storage…
I really hate it when WP ‘half ins’ these sort of things – makes it hard on us plugin developers… they should have either gotten rid of it for all users or left it…
at some point, when we do our tighter integration with wp, we hope to find the best way to handle this with new installs that may not have or want a blogs.dir…