What type of solder are you using? One reason for this may be that the solder being used is not pure. Inexpensive solder sometimes leaves residue. Sometime you can clean the particles out but it is easier to buy quality solder to begin with. Another reason is that spots are often caused by dirt or other particles caught in the solder. These can often be removed when you wash or buff your piece when it's finished.
You should not dip your flux brush in the bottle the flux comes in. Constantly rubbing the foil with the brush and dipping the brush back in the bottle contaminates the flux and causes all sorts of soldering problems.
Get a new bottle of flux. When you're ready to solder, pour a small amount (like a tablespoon) into another container. Use the flux out of there. When you're done soldering, dispose of the remaining flux in that container. The flux in the original bottle will remain fresh and uncontaminated.
Wet a paper towel and squeeze it out so it is only damp, not soaking wet. Fold the towel into a square. As you're soldering, frequently wipe your soldering iron tip on the towel. That will keep your tip clean.
An excellent source for solder which is American-made, free shipping, and excellent customer service is <http://www.ebay.com/...er/172783866711> Make sure it is coming from Hutchins, Texas.
I hope you have better luck on your next project.