Jumps forward when brakes are applied at intersections when stopping Doesn't happen all the time.

I don't know if this would be considered a solution or not but in 2006 Ford implemented a new transmission (6 speed automatic) and they have and still have a lot of problems. It is fixed (helped may be more appropriate) by a computer upgrade done by the dealership. MY wife has had nothing but problems out of her 2006 limited ford explorer. The whole computer system had to be replaced at 32,000 miles and then they charged us to upgrade the new computer they put into the car. It's almost comical at this point. The transmission problem has been solved for the most part on our vehichle but it took several ford computer updates. I hope this helps!

Probably your air conditioning turning off which means less load on the motor plus a few more revs. You then need to put more effort on the brake pedal or the car will go forward. It's like putting your foot on the accelerator pedal.