You could modify the organizer (or any other) post type after it is registered, using the registered_post_type hook – although it’s beyond the scope of support to walk through that if you were to make a feature request (for organizer and venue slugs to be made editable) we would definitely consider it.
You can add feature requests here: https://tribe.uservoice.com/forums/195723-feature-ideas
Aside of that, when I update a Local/Organizer I get a link to View Local/Organizer, but when I click the link I get a 404 error. Is that a known bug?
Nope … I’m not sure why you are experiencing that. Can you visit Settings > Permalinks (you don’t need to adjust anything – simply visiting that page should refresh permalinks) and then see if those pages are accessible?
If they are not, though I note you marked down that you had already tried this, can you try the following steps (or if you have done them already let me know what the outcome was):
* Deactivate all non-Modern Tribe plugins
* Make sure your Modern Tribe plugins are up to date and in-synch (if you are using The Events Calendar 3.0.1 then you should use Events Calendar PRO 3.0, for example)
* Switch to a default, unmodified theme (such as Twenty Twelve)
* Does the problem persist?
* If it does not please reactivate everything one-at-a-time
* Should the problem return, please note down the last plugin you activated before it came back
Thanks!