I fly one with MT-Propeller supplement and it does 125 KIAS at 75% power any day, anywhere (Vno 118 KIAS though)
And the best part is that climb performance isn't very much different from Sensenich's prop, around 800-900 fpm at MTOW (Vy+5).
DA20 is also very good for spin training, but you have to hold the controls fully crossed in order to maintain rotation - but you should be aware you have to pull up when rotation stops since it has a tendency just to accelerate to the ground...
I agree with B2N2, the engine cooling in fast cruise is a major issue, you actually won't get CHT in green unless you do some major climbs below Vy. They should have built in a cowl flap, but I guess they considered aircraft as primary trainer for ab-initio and climbing with fully closed flap (which a student might do) wouldn't do engine any good. As far as I'm informed, cylinder head cracking due to overcooling is quite common on -C1.
As for hot starts, they are a quite b**** since the moment you stop the engine, its temperature initially begins to rise (and not fall as you wold expect), due to lack of cooling airflow from the propeller. This causes the fuel to turn into vapour (especially in fuel injection pump), which causes lack of fuel flow during hot starts and thus preventing the engine start. The Continental's solution stated in IO-240 Operation manual (sadly not incorporated into DA20's) is that you run boost pump for 15-20 seconds with throttle closed and mixture in the idle cut-off position and then perform a normal start.
General handling is quite good, very responsive on all axes, pitch trim could be better (bettter than PA38 which also uses spring-type though). Certainly DA20 gives you much more work to do flying it straight and level than C172, but I just adore the aircraft due to its speed vs. cost ratio
P.S.: Is it just on DA20 I fly or are the pitot/static instruments (ASI, altimeter and VSI) very "jumpy"? It's almost impossible to maintain constant (accurate) vertical speed or airspeed...
