These are all pertinent questions to think about when you write a blog that you hope people will follow. Weed the Garden if you want to keep it looking good. If your links are dead, your article loses some of its meaning. I recommend checking archives, but I know that is time consuming.
Here is what I do: When I'm writing an article about a particular topic that's related to early works, I check out the links in the archived article BEFORE I include a link in the new article. This is a great way to find dead links. It's surprising how many websites change their actual names for their web pages.
Checking this links is very important for another reason. It is the way that you cite your sources, so it's critical to keep these citations current.
I wish there were some dynamic agent or web app that could check links, but I don't know of one. Do you? If so, it would be wonderful if you would share it here.