Users can edit old posts, adding links to whatever they want, and there's no way that a forum administrator would know about it.
As far as I know based on a bunch of testing, editing a post inside a topic doesn't push it up to the top or make it unread even for people that read the topic or were replied to by that post. And you don't need to have special privileges to do it (I edited a couple of my own old posts here on Meta while testing).
Why this is bad:
Any user that happens to reply to a topic that ends up being popular in Google can go back and add all the spammy affiliate links or SEO links that they want. Nobody is going to check the links in old forum posts, especially if they are integrated into the paragraphs well. Or if the good links are just swapped out with bad ones.
Why this could be really bad:
Users that achieve Leader status get all their links followed for the search engines.
This means that all you need to do is consistently be a part of a forum, or many forums, for 100 days or whatever the time limit is. And then you can go back and edit all your old posts that have been strategically placed on topics that are likely to be popular. SEO links? Sure thing! Affiliate links? Check!
Look at that, we've created new jobs. Take that, politicians!
And if you don't think there's good money in spammy SEO linking, you clearly haven't run a website that has a lot of search engine juice.
How this can be fixed?
This is where I'm not entirely certain and would love to see ideas from others. (Obviously disabling the search engine follow link feature would be a good start)
Perhaps there should be a setting to notify moderators when somebody adds a link to an old post via an edit? I imagine that could be a pain. Bumping the post to the top would probably be really annoying for everybody.
And Yes, I'm aware of the post edit time limit setting, which I've set to 14 days on my forum to at least try and deal with this problem. I think the default is one year for new forums though.
That change is not really a solution as much as an annoyance for the regular forum users though, and for a really busy forum, topics from 14 days ago will be long forgotten.
I would much rather allow people to edit posts for longer than 14 days. I'd also love to see affiliate links dealt with.