Now that this has had time to rattle around in my brain, I think the best choices are 1) to have janitors make minor fixes where appropriate (consideration is probably the best way to submit requests for such). If more extensive "improvements" are warranted, then 2) someone needs to make those improvements and when they finish them, they just need to post the new version like anybody else would (and include a link to the original) and the pedagogues will change the link in Tutorials to point to the new version.
In the unlikely event of a group of more than 1 person effectively taking on joint, on-going responsibility for extensive changes to some tutorial(s) (seems very unlikely), we can consider a wiki-like tutorial. No need to burn that bridge until we get to it.
As for what is appropriate for janitors to do to Tutorials, my first stab at a guiding principle is to respect the authorship. That is, objectively technical corrections should be inbounds and nothing else. And if the correction can't be adequately described in the small "consideration" text field, than a reply is probably a better first step.