I think this is not a particularly big problem given the nature of most common links in this site.
Regarding your two examples, Wikipedia and arXiv updates are natural and linking to an old version is bad practice. If the Wikipedia edits are radical enough that the original point is lost then there is always the edit history both on their side and ours that it's possible to reconstruct what the original link was. ArXiv edits are very rarely substantive enough to remove crucial information, and if they are it is a strong indication that that content was unreliable (and, again, there is the edit history to fall back on).
For other links, it's more of a case-by-case thing. The Wayback Machine now enables visitors to archive pages (unless forbidden by the site's robots.txt file), and it is generally good practice to make sure that the Wayback Machine has a suitable copy archived before linking to a webpage on this site, and particularly if the link looks susceptible to link rot. However, the link should always point to the current live version. If the link rots in the future, or the target page changes, then the link can be re-directed to the archived version if and when than happens.
Another class of links which is more fragile (if relatively less common on this site) is YouTube videos, which can disappear for a variety of reasons and leave essentially no traces behind them (stable image). If you're linking to a video, make sure that the video's title is preserved either in your post or in an archived version of the page. Archival services, in general, won't archive the video, but they make it possible to understand what the link was and, if there is an equivalent video available, to redirect the link to the new location.
So, in general, here are some guidelines for when and how to take active steps to prevent link rot:
- Always use DOI links when linking to online articles. A Digital Object Identifier is a permanent link and will always follow the document, while journal website urls can change and even be inaccessible to users in other locations. Find the DOI marker on the page, e.g.
doi:10.1038/nature12422, and link to http://dx.doi.org/10.1038/nature12422. For books that don't have DOI's, a good alternative is an Open Library url.
- While we're at this, when linking to the arXiv, link to the abstract page (arxiv.org/abs/...) and not directly to the pdf. This is a courtesy to users on lower bandwidths and mobile browsers (which can automatically redirect to separate pdf viewer apps), who can then evaluate, from the abstract page, whether they want to actually download the paper.
- If the paper has been published (which will be noted on the arXiv abstract), include a link to the journal version, even if it's paywalled, if only as a courtesy to the referees' hard work. In some fields of physics it is standard practice to upload the last, published version to the arXiv, but this is not true in all fields. Moreover, journals collect download and usage statistics and make them available to the authors, which the arXiv does not do. In any case, linking to the official, journal version (as well as the arXiv!) helps the author by improving the search engine ranking of their paper, and it probably helps us in that regard as well.
- If citing a pdf of a paper or similar that is not on the arXiv or a similar repository (e.g. a university repository), use a web citation service to protect it, ideally the Wayback Machine, or at least make a local copy.
- When citing Wikipedia or the arXiv, always cite the most recent version. Revisions will most likely be improvements, and if it is unclear what the reference was for there is enough edit history to reconstruct that.
- When citing external websites, always cite the page's current position, and make sure that there is an appropriate version of the page in the Wayback Machine.
- When linking to YouTube or similar services, make sure that the title and other information of the content are preserved in your post, to make the linked content easier to trace if it vanishes.
Demanding permanent links is rather too harsh and will slow down the site, particularly with new users. If someone posts a particularly fragile link, change it to a more permanent one (using WebCite, the Wayback Machine, or similar if appropriate) and refer them to this question. More experienced users should be proactive in editing such links when they look fragile.