those are most often referred to as sparkles.  The fixes include the following.

Tweaking of a few of the voltages on the Y sustain board.  These adjustments are often only a temporary fix.

Replacement of the X and Y sustain boards along with the Logic board.

Finally, if these do not solve the issue you'll have to replace the PDP panel itself.  Not cost effective in most instances.  

Since this is an "R" model, HP"R"5072, it is about 3 years old and out of any manufacturers warranty.  The real pain with making any adjustments to the set is you have to lay it down, remove the stand, then remove the back, then put the stand back on and return it upright so that you can see the picture as you are making any adjustments.  Being a heavy 50 inch plasma set, this is a 2-man job.

 If you want to tackle it, remember you will be working with the back off and the set plugged in.  There are voltages that can kill.  The plasma panel will be marked with a set of numbers in the upper right hand side reading Vs, Va, Vscan,Ve, etc...with the values that your panel will need-  each panel is unique and tested when manufactured and marked.  The important ones are Va and Vs.  The place to measure these will be on the SMPS board in the middle.  The measuring points and adjustments are on the upper right corner of the board.  IIRC, Vs may be somewhere around 185Vdc to 197Vdc.  If the set is even 2 or 3 volts higher than the marked value, the set can sparkle.  It is best to set this 1 to 2 volts less than what the panel is marked.  Va is something like 65Vdc.  Once again, set it 1 to 2 volts less than what the panel is marked. Set these when the set has been on 20 minutes and is warm.

Check the picture while and after making any adjustment.

Why did the set begin to sparkle?  Could be any of several reasons.  The SMPS could be regulating a little higher with age.  The plasma gas can be aging.  Your incoming AC could be higher from the power company. Maybe the young lady assembling the set and calibrating it when it was built left the adjustments a little high to begin with.  Or her DVM was a little out of calibration.  A combination of any or all of the above. Who knows?

IF ADJUSTMENT DOES NOT CLEAR THE SPARKLES, you may need either a board replaced (SMPS, Y-main, or X sustain are the names Samsung uses) or a display panel replacement as MOtvGuy said.

In answer to your last question, could happen to any plasma set...

Folk, my Samsung HP-S4253 , 2 yrs old on 9-16-06 is getting all types black, red, blue dots. If you turn it on and back off the dots go away for a period of time. Samsung said this was