How do I "fix" a bad sweat (solder) joint?
Just heat the joint up with your torch, once the solder starts to melt use Channel locks to pull the fittings apart. Once the joint is apart, wipe as much old solder off as you can with a rag. Now you can start over. Clean, Flux, solder. 

You should not be applying flux to joints you are not working on, take each joint one at a time. If the joints are all close to each other, try doing the joints out of order. Solder one joint, then move to a joint further away, then back to a joint near the first, etc.  This should allow some of the heat to dissipate, and reduce the chances of overheating the joints.

Don't forget to wipe excess solder off the joint before it cools using a damp rag, nothings worse than an ugly joint (except maybe a leaky joint). And don't forget, soldering pipes is an art. And like most things, it takes lots of practice to get good at it.