I have a similar issue with the same PIR from Parallax, but I worked my issue down to my UNO being powered by the USB. I used the testing circuit provided by LadyAda in her sensor tutorial http://www.ladyada.net/learn/sensors/pir.html
. It is pretty simple and should be fool-proof. I powered it using the 5v and GND pins on the UNO connected to the USB only, but I would get false readings from the sensor. The issue disappeared when I used an other power supply to power the UNO. I could get a constant 4.99vdc from the 5V pin with a 6V dc power supply, but I got a bouncy 4.95-4.97vdc with the USB.
The PIR is designed to work with a 3.3 vdc power supply, so I set up a variable Power supply to 3.4vdc and the sensor picked up normal movement, and it did not send out random signals. I had to use my meter to get the output changes as the OUT signal from the PIR was down to 1.6 v with the reduced input voltage. Just to be thorough, I checked the voltage on my Vin pins when it was on USB, and I got a voltage closer to 4.6 V and the same false readings occurred.
Is there a trick to cleaning up the power from the USB on the UNO, because I also ran LadyAda's Arduino demo at the bottom of the page and had the same flaky signal.