Hi Guys. This is such an interesting thread that I thought I simply must bore you all with my observations!
I remember us not that long ago thrashing out the exact meaning of "expedite" (best RATE of climb in the UK), but that in practice most pilots I have flown with dial the speed back and achieve something approaching best ANGLE of climb as trytofly mentions. In fact, I don't even increase thrust in the majority of occassions.
As a UK pilot I have absolutely no problem with the term "expedite". Controllers in the UK (as I have mentioned before) use heading much more frequently than other units in order to provide separation and expedition of the level change frequently helps both parties. The fact that exact rates are not given does not matter as separation itself is not predicated upon a particular rate as the aircraft tend to be pointed away from each other.
I personally dislike the ROC/ROD type clearances issued by Maastricht, Rhein, Langen etc. When they are issued I have no idea if the aircraft is going to be able to achieve it - there are no tables published and the FMC is no help. I am relying on experience. The 757/767 has a vertical speed (V/S) mode which can be used to fly these clearances, but it offers no speed protection, so the risk of a "low/high speed event" is increased. The problem is further magnified by passing through a jetstream or the tropopause etc.
For me "expedite" is useful as it retains control of the aircraft's performance within the flightdeck yet encourages a quicker solution to a separation problem. (Unlike "be level in 2 minutes" or "speed 290kts, 2000fpm or more")
I don't think that "expedite" needs its definition tightened at all. I like the room for interpretation. If my wife says to me "hurry up and put the shelves up and I'll drive you to the pub" I still have control over how long putting the shelves up takes, but it is clear that doing it more quickly than I am currently will help everyone!
Just my thoughts
G W-H