The Quickfix, best god damn weapon I've played with. And it doesn't even kill people.
My thoughts/analysis of the weapon:
If you are a pocket medic, use kritz or medigun, this is not the gun for you. The QF is a group weapon, what it lacks in direct offensive buffs, it makes up in group healing. With the uber (+300% healing, immune to movement impairing effects), you can keep a group of 4-5 healed very easily, especially if they are groupped together. Example: I was on Egypt 1-1, 2 pyros ambushed us on the point, there was a group of 4-5 with me, they were all set ablaze. Not only could I keep them all fully healed while in direct fire (pun), both pyro's died, and everyone was back at full health in the end.
The Speed boost, although, not used a lot because medic is faster than most classes, can be really a helpful way to rush to the battle field/move around and manuever and take cover. A couple of times so far I've tagged onto a mid/low health scout and "slingshotted" myself to safety. I have yet to try and tandum with a multi-head Demoman.
The QF is very versatile for most gametypes. The only times when its less effective (not useless, but not as effective as it can be) is plr and attacking in PL. Arena is sorta included on that, depends on how good you are with arena. The reason for this though is that if your attacking, your around the cart, which provides healing to people anyways, so its not necessarily good, but can be effectively used to help clear out area's that the cart will be going into to, and to provide pressure on said defenses. Its also not very effective in smaller games (like 6-8 people per team or less)... for smaller teams I'd suggest Kritz or Stock Medi. I am interested to see what the PvP community does with it...
I'm not going to say this requires "skill" to use effectively, but it does require an understanding of what the medic's role is in a team, and some basic intelligence.
EDIT: I forgot some points to add, so I added them. (Para 3)