There is an update for the monitoring application: it now visualizes the internal PID parameter dPV/dt as arrow. For demonstration, a setpoint step change:

(save and play with quicktime)
The arrow indicates the internal dPV/dt term of the PID that looks to the future. Ideally, the arrow would be a continuation of the curve as is obvious to a human. That's not so easy for a PID because it works in small intervals. In each of them, the temperature change rate is close to - or below - sensor resolution. Add noise, phase shift by filters etc. and it can add up to significant inaccuracy in the differential term.
With the trend arrow, one can now see easily how large the difference between the human-recognizable trend and the PID's internal calculations is and if there is a problem with resolution, noise, settings for filtering, cycle time, differential quotient etc. If the arrow reasonably matches the apparent trend, parameters are acceptable. If not, one has not found good setting.
Below is a link to another video I made while checking the arrow function (zoom level change in second 104 shows more details):
http://emc.awardspace.com/videos/forum_brewdrop.mov It's a 25s shot. A free-floating thermocouple is installed 2mm under the brew head of a Gaggia Coffee (no portafilter) to measure the temperature of the escaping water over 25s. As you see, with an electronically adjusted flow rate of 160ml/min, the temperature of the brewing water drops by about ~2.5 degrees. That's a bit much but on the other hand, 160ml/min is more than a typical espresso shot. Anyway, I'm posting the video because it looks as if there is enough potential left in the heating elements to compensate for the temperature drop by feed-forward control.
(the jaggedness of the water sensor curve is due to the wacky measuring method: free-floating thermocouple reacts violently to air bubbles in the flow, every breath of air and drops of water and steam from the brew group).