Supporting multimedia codecs via open source implementations is not against any free software purists ideals. It's the software patents that put halt to distributing such distributions should this kind of more minor distribution become big at any point of time.
I believe they probably also include Adobe Flash, hopefully via the same downloading system Ubuntu does instead of any "we just ship it". That's proprietary technology which includes proprietary codecs, but to just write "deliver proprietary multimedia codecs out of the box" is quite wrong when also Mint probably delivers most of its multimedia codecs via Free implementations which just happen to be patent-encumbered because of the current (stupid) legal system.
Anyway, more introduction to Mint would have been welcome. I do know it's based on Ubuntu and it contains considerably more work than the 10 other Ubuntu-based "we changed background!" distributions, but still. History, infrastructure, security updates to those software they ship from their repositories instead of Ubuntu's (or do they have completely own repositories?) etc.