If a site has a high PR does that apply to the entire site or just one particular page?
In other words, if www.mycompany.com which has a PR of say 5, has a page called www.mycompany.com/links where has a PR of say 0 and I have a link on this page to my external website. Does this mean I am effectively getting a link from a worthless source?
I think your asking the wrong question. If a site has high pr there is also a good chance the entire site has good authority. PR is based on links. Home pages normally get the most links. Each page that the home page links to has a less PR and the pages those pages link to have less PR. If you have links to internal pages it works the same way.
The goal is to build up authority so that the authority passes down. Authority passes down more value than PR. If you website has authority then all of your pages have a better chance of ranking.
If you do your internal linking correctly then you can pass around PR better. When I speak of PR i'm not talking about the toolbar PR because that does not mean much. I'm talking about the PR value that Google assigns to pages and does not tell us. Your internal pages need to link to each other using anchor text. If you want to see a site that does this perfectly study wikipedia.