Of course this depends on what kind of site you have for whom. A company might not want to add too much content and might not want to remove older material either.
A forum is another beast. Pruning threads is in itself not a bad idea. If those are all "hi I'm new!" threads than I don't see it negatively impact search.
Purely working on gut feeling I would say that on a forum this large the gain in internal link distribution is similar to optimizing meta tags: if all is equal it helps a bit
Let's say you have a site with a few hundred decent links. That might be enough to make a powerful niche site but if you had a site the size of wikipedia then you would have a ton of pages that don't get enough spidering to stay healthy in the index. I think that some of the juice would disappear into those deep pages and none of your pages would rank very well.
A variation of the "bleeding PageRank" idea?
I don't really believe in that. My view remains that every page is a site. For most purposes sites don't exists; only documents. If page A on your site has a given weight (call it PageRank or whatever) and you use that weight to vote/lift other pages, then page A itself does not lose
Also, site A does not become a powerful player in a niche: single pages on site A do. Is page A ranks well for "mini widgets", it will continue to be ranked high for that term whether or not site A consists of just that one page or 100 pages.
Nor do I believe that regular spidering = healthy in the index. Google uses various factors to determine if they should check a page again and if so, with which priority. A document which remains unchanged over a period of time, functions as always and has no inbound link patterns which suggest a change needs to be spidered less often than one in constant flux.
The blog that I am working on does news commentary and reviews. Lots of the pages now link to dead URLs or redirects on other sites. What should I do with those post pages.
If this is a more or less consistent pattern, as can be the case with many news stories which disappear within 2-4 weeks, than you can use an automated solution. After 2-4 weeks remove the link or replace it with a search for the title of the original item.