For example, the edit http://musicbrainz.org/edit/19813802 is stuck, because at the time of application there was another artist called 'August Heinrich Wenck' with no disambiguation comment.
Isn't this just a duplicate of MBS-5585? It's the same problem, it's just that auto-editors get the error immediately while non-auto-editors get edits which can't be applied.
Not quite, because this actually crashes in ModBot. I imagine it will get resolved at the same time, though it sounds like the other issue needs some sort of check before entering the edit.
In review at https://github.com/metabrainz/musicbrainz-server/pull/41
This fix seems to be what's caused the error listed at MBS-5873.