Why isn't it common for papers in pure and applied math (and other related fields) to be modified/corrected after it has been published?
The primary reason is that journals are &quot;publications of record&quot;. They just record a specific version of a paper, namely the one that actually gets printed, along with important data such as who wrote it and when it was submitted.
You are of course free to put corrected versions onto your website, or maybe onto preprint servers. But in the end, that's not the &quot;version of record&quot; as you can change whatever you want on it -- you can add and remove authors, etc., and it's hard for anyone to track down when exactly a particular change was made if a dispute should arise who came up with an idea first. It's of course true that journals today could just do that on their websites: allow newer versions of papers to supersede older versions, but then that would require some kind of editorial process that journals are not equipped to handle.

Completely separately, though, I take issue with your opening statement: &quot;very few reviewers now have a complete picture of any single field. Thus it should be common for more mistakes to be published&quot;. I don't think that there is proof that that is true -- science was difficult 50 years ago, and it is difficult today. I don't believe that authors or reviewers or editors are any worse equipped today to assess the contents of papers than they were 50 years ago, and so I see no reason why we should expect more mistakes.