I know that one is not supposed to write this in a bug report but I have to make the point clear:
It is extremely important that this bug gets fixed because currently all redstone circuits/contraptions that use sticky pistons are broken or at least don't work properly.
Especially now that we've got the opportunity to create sticky piston based instant logic gates without the usage of any bugs like before, it is quite annoying that this ruins all of it.

When a sticky piston is powered and the signal strength of the redstone attached to it changes, the sticky piston pulses (contracts for a short time and then extends again) even though it should stay extended all the time.

But this does not happen everytime, it depends on how the signal strength changes. I've gone through all possible ways to change the signal strength and created a list where all 47 combinations of before (old) and after (new) signal strength values are listed that cause the sticky piston to pulse.
I tried my best to find a rule and created a little algorithm that tells you for every new signal strength value which old signal strength values would cause the sticky piston to pulse. This algorithm still has 5 exceptions and does not make any sense at all. This brought me to the conclusion that this definetely has to be a bug.
Since these combinations are so random, it is basically impossible to build a redstone circuit with sticky pistons and avoid this bug from happening.
You would have to place the redstone so that no matter what the situation is, the change in signal strenth in front of any piston included in the ciruit would not be one of the listed combinations.

I attached a .txt file with the list and my pseudo code (algorithm).

Me and the complete redstone community hope that this bug gets fixed before Minecraft 1.5 will be released!

EDIT EDIT EDIT
It actually IS a randomly occuring bug. There is no way to know exactly when the sticky piston pulses in every situation.
That makes building redstone circuits with sticky pistons trial and error. So it's even more important that it will be fixed.