LarryD:
I use Isopropyl alcohol to remove the residue, before the alcohol evaporates wash the PCB in distilled water, then use an air compressor to blow off the water.
Things like switches, relays etc. that can be damaged by water, are soldered after.
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I usually use a cotton swab with Isopropyl Alcohol to clean up after soldering etc. with rosin core solder (or before soldering to make sure I get any grease/oil etc.). Be careful with the air compressor - many of them will have some oil in the air and end up contaminating the work area with oily air (that is why you can buy all those oil/water separators). A diaphram type compressor is usually pretty clean, but if yours is like mine (2hp piston type), there is some oil in the air (blow it on your hand for a bit then rub your hands and notice the slight oil film). Another issue with high pressure air if you are not careful - things like O-rings seal by pressure on them and while they can withstand quite a bit of pressure, fast moving air etc. does not give them a chance to seal and will sneak under to get inside (used to have that problem with diving watches where they were good to 200+ feet, but would flood in the shower where high speed water drops hit the seal and went under it. They changed the design of the buttons so it can't do that, but it used to be an issue.