One of my main gripes is the ability to atomically update an issue vs incremental updates. For example, Bugzilla allows you to edit multiple fields then hit commit to save, Jira on the other hand applies changes automatically when you edit certain fields (e.g. assignee). This causes people problems (person gets assignment email before the comment about why it was assigned to them has arrived or vice versa), and automation problems (if you have anything driven by receipt of the emails, you now need to collate many before action can be taken). It may well be possible to configure Jira in a way that's more useful to us, but sadly we've got one mega instance that's supposed to be all things to all people and as such, doesn't do many things well!
Used Redmine before Bugzilla and thought that was pretty good.