Ok, so you are seeing every increment as a major version change then.
I think semver helps to be explicit about what the version number
actually means. I guess in part I'm trying to understand why fixing
bugs involves a major version change, and breaking backwards
compatibility.

version here is not for notification, its for the client to specify what it expects the behavior to be. Fixing bugs does not change version, not unless there is a *breaking* change - if we decide to obsolete ver5 and start ver6 due to inability to include new features. This is a very rare occurrence. APIv1 lasted for 6 years and still going strong :)

Mark Nottingham recently wrote about semver, REST and how to evolve
Web APIs [1]. I think developers are increasingly familiar with
interacting with REST style APIs (Amazon S3, Twitter, Facebook, etc).
In general REST APIs encourage simpler documentation, easier
cacheability, and can often make the need for 3rd party API libraries
disappear, if a good HTTP library is available.

A change to the major version of the Mediawiki API might be a good
time to think make a fresh start and think about the API in this
way...or not :-)

Make a proposal, we discuss, and than we start throwing rotten tomatoes in a different direction ;)