First - sorry if this thread is useless to most people. I know, however, the number of players having issues with
hair speckles did not begin and end with myself.
I tried some things with the graphics settings, and found that turning off Smooth Edges eliminated the hair speckles. However, it made everything else look jagged and unpleasant.
So, if you have an nVidia card -- and/or, assuming ATI has a similar control panel -- go to said control panel, select Sims 3 (ts3.exe) from the available applications (if what you get is Sims 3 Launcher, and when you try to manually add ts3.exe to the list and still end up with the launcher, you need to uncheck "Show only programs found on this computer", ts3.exe will then be listed there.)
Where is says "Anti-aliasing - Transparency" turn that manually to "Off". Done. No more white specks and you can keep smooth edges on so nothing gets jagged.
TL;DR?
To get rid of white speckles in Sim hair, turn off anti-aliasing transparency.
Hope that works for everyone else...