Burnishing pens are good, but a Garryflex block is almost as good for general clean up and won't leave those lethal little fragments which impale your finger ends.
Lolly sticks are also good for holding items while you solder - use them as insulating pads between the job and your fingers. Bits of balsa will do the same thing, or you can stick components into them while you attach other parts.
I'm not sure cleanliness is your problem - it looks to me as though there's not been enough flux or the iron wasn't hot enough. What did you use for both?