All good questions, I'll try to answer them one at a time:
not being able to see comments on a blog post
Can you check the permissions in the admin console --> spaces --> permissions --> space permissions --> Read Comment? Who has it assigned and who doesn't?
can't figure out how to restrict blog visibility to specific spaces
You can't restrict a single blog to being viewed only in a space, you can however restrict the viewing of a blog to only members of a certain group. Go to the admin console --> blogs --> select the blog you want to restrict --> click edit --> edit blog permissions.
An additional issue is that anyone who registers can start a blog
This is an easy fix: go to the admin console, click on the blogs tab, click on the permissions tab and remove the ability for registered users to create blogs. After that, you'll just want to assign the 'create blog' permission to either a group or a single person at a time.
I gave permission for folks to read comments in the Spaces area, but they still can't read them. Any ideas? I'm on 1.0.3.