From feedback we get repeatedly as a development team from interviews, user testing and other solicited and unsolicited avenues, and by inspection from the number of edits by newbies not quite aware of the impact of their edits in terms of immediate broadcast and irrevocability, that new users don't necessarily understand what "Save" on the edit page means. Yes, there's some blurb underneath, but (a) it's not clear, (b) it's (necessarily) filled with jargon, and (c) it's in the traditional "blurb blindness" spot where no-one pays attention.
In user testing this has been particularly highlighted as a point of confusion for new users. Even though "user-generated content" sites are a lot more common today than they were when Wikipedia was founded, it is still unusual for most people that their actions will result in immediate, and effectively irrevocable, publication.
Many other wikis use "Publish", notably including Wikia in their fork of MediaWiki since (?) 2008 or so. Most other similar tools use "Publish" for this action, and reserve "Save" for server-side drafts (something we're unlikely to provide right now, as discussed elsewhere). Re-labelling won't solve all issues, but it will more clearly and obviously declare to the user the nature of the action they are about to take. It may reduce slightly the rate at which newbies make their first change, but hopefully because they are more informed and accepting of what they are doing.
However, changing though trivial in terms of code will be a very visible, and possibly mildly disruptive, change to a lot of existing users' workflows, so we should consider carefully this change and not just rush in.