I mean ideally we shouldn't be showing any modules on the site error page (we don't know where the error came from that took us to the error page - so it's best that we keep exposure to any extensions to an absolute minimum). So beeze actually only loads the menu module position and the search module position - whereas protostar actually loads a significant number more modules (not necessarily a good thing as I just described) so I'd just call the difference between templates as "expected behaviour)
As for the style bug I'd suggest that the bug with the list is going to be related to the order we load the CSS files in the error page (at a glance seems different to the index.php page) - but don't have the time right now to test that.
I would guess tho that whilst bugs these will have been around for a while and I definitely wouldn't call them blockers (although for sure the styling is a "nice to fix"). Can you report them on the tracker please Leo?
Kind Regards,
George