On the main site, link rot is a potentially serious problem. It can turn otherwise meaningful questions and answers into nonsense. However, it's a problem that we can mostly avoid. First and foremost, note that links on this site should never be crucial to understanding a question or answer. The post needs to be a self-contained question or answer. Links are primarily used for the purpose of supporting claims and referencing sources, but any relevant content from that source still needs to be part of the post here.
If you see a question or answer that you need to click a link to check, chances are quite high that it's not a real question or answer (yet). If you feel like it's easily salvageable, suggest an edit copying over whatever content is needed from that site to make the answer here complete. Otherwise, vote to close or flag it or leave a comment for the OP. If the content of the post doesn't contain enough information to constitute an answer, you can flag as "Not an answer". For example:
The answer to your question is on this link
In this case, there's no content to the answer. You have to follow a link to get to the content. So it's not an answer. It either needs to be edited or deleted. However, in some cases, a short post with a link can still be an answer, so use some common sense and check if the content in the post is enough to answer the question.
One special case of this is images, because embedded images are sometimes crucial to understanding a question. For this reason, any images should be uploaded to the stack.imgur. Such images are backed up regularly. Images which are not uploaded via this can potentially rot.
If you encounter an already rotted link, you may be able to find a cached copy e.g. with Wayback Machine. If you can, then you can edit the post to use that link instead or remove the link entirely if it isn't crucial. If there isn't a cached copy, the link should just be removed since it's of no further use. If the content isn't accessible and the link was needed to make sense of the answer, then the answer should be deleted since it's not of any use, but this situation can be avoided by being proactive with the above steps.
Here on meta, link rot isn't such a big concern, because meta is very low traffic. The average post here gets only a few views per month. There's nothing wrong with commenting on the post or flagging it, but it's usually not that important. If you see a post where all of the answers are completely invalidated because of link rot, there's a good chance it might be time to re-discuss the topic anyway. But if it's just a link to an Area 51 proposal (which disappear regularly), it's usually fairly tangential anyway and not a big deal if that link rots.