According to some articles, if you'd like a clean PCB - it's better/safer to use a solder/flux that is designed to be cleaned (e.g. water soluble), rather than try to clean a no-clean solder or flux. The idea is that the no clean solder is designed to encapsulate the corrosive chemicals, so it winds up being harder to dissolve and clean.
I've definitely found this to be true. It's far easier to use water soluble solder/flux and clean afterwards for a good looking assembly.
Also, beware that toothbrushes can cause static electricity - horse hair bristles
are what's commonly used in industry to avoid the ESD.