1 - Should I be dropping these "less than valuable" links?
If you feel they are "less than valuable", then yes, you should be reviewing and purging those where necessary.
The reason I used the intentionally ambiguous "less than valuable" description was to read some opinions about what types of links are valuable.
2 - Should I selectively add <rel="nofollow">?
Red flag. I wouldn't touch that attribute with a 10 foot pole unless of course I had a blog or similar outlet. The whole purpose of that attribute was to curtail blog spamming.
I'm curious about this statement. I have seen numerous recommendations for using <... rel="nofollow">. Just because something is designed for one purpose doesn't mean it is necessarily inappropriate for another.