I use a PID from Auber Instruments. Given my current calibration, I have found that I have to set my temp 2 degrees below my target, let it overshoot, then about 20 minutes into the mash as the temperature has stabilized I can slowly raise the PID up the final 2 degrees. That generally keeps me right at the temperature I am looking for. I originally set my probe at the inlet to my RIMS tube, but have moved to directly in the mash. I found that given the thermal mass of all the external equipment the RIMS tube temperature fluctuates much more slowly. It can take up to 10 minutes for the 2 location to agree on the current temperature. The mash will rise at almost 1 degree every 45 seconds when the heater is continuously on, but the RIMS tube measurement reflects a 1.5 to 2 minute degree changes.
Personally, I do not worry about the temperature of the wort as much as the grist. My theory being that I am more worried about the enzymes in the grain. Whatever is in the wort is already dissolved, and does not need as much conversion. I know that most HERMS brewers are concerned about killing the enzymes by running the wort past a heater element. I always see efficiencies of 75 - 80%, and have never scorched anything. I do keep the pump running at all times.