A recent thread on the wp dev mailing list brought up the fact that some people have a hard time understanding 24-hour time and so are confused by the editor's usage of a 24-hour clock when modifying a post's or page's timestamp.
One potential solution for this issue is to make a profile options which lets a user change the way the editor displays its timestamp.
If this option is set to 24-hour, then the editor behaves as it does now, displaying the timestamp in 24 hour time e.g. 17:43. This option is the default in all cases.
If this option is set to 12-hour, then the editor displays the timestamp in 12 hour time e.g. 5:43pm. The user can then change the time and the meridiem (am/pm) using a dropdown box.
All internal representations of a post or page timestamp remain unchanged. Only the display of the timestamp is changed if the user chooses 12-hour time. In this case, code in post.php converts the time back to a 24-hour representation before committing the change to the db.