Red dots like"snow" are all the way across the screen when dark colors are present on my 1and 1/2 yr old toshiba 50HP66 tv.

If they are moving, it is a Random pixel discharge. This can be caused by 3 different problems, that are not easily diagnosed through a chat like this. 1. I could be a miss adjustment of critical voltages that control pixel discharge in the set, although i have not looked at your set in particular, some models are automatic and don't have an adjustment. 2. It could be the x board or equivalent, 3. It could be the panel it's self.

in my experience with this problem the adjustment rarely fixed the problem, more likely the Panel is failing, although sometimes the x board will cause this issue.

I am sorry I cannot get you any closer than that, I recommend getting a repair tech out to check it out. This set is repaired by replacing boards not component level, the boards can be expensive and I don’t want to recommend a board replacement unless I was the tech to actually see the problem.