Some report breaking pieces of glass while soldering. This may happen more on pieces that have big differences in width or taper to thin points. What is happening is that the glass is being heated too much locally in relation to the rest of the piece.
The solution is to solder at a steady pace. This allows the solder to cool without transferring so much heat to the glass as to break it. Some recommend that you do not rest your soldering iron on the foil while soldering. However it is the solder which is the heat sink, so the effort of holding the iron above the foil is not really necessary if you move at a reasonable pace.
This means that you do not stop with the iron on the seam. It is best to solder in one continuous movement along the seam, leaving an even bead behind. Sometimes the bead is not even. This may be because of wider parts to the seam, or inadequate flux, or many other reasons. Do not try to repair this before going on to the rest of the seam as this builds up heat in the adjoining glass. Since glass cannot dissipate heat well, the glass breaks when the temperature differential between the hot and cold parts of the glass is too great. Instead, complete the soldering of the seam before coming back to it. This gives you time to decide why the bead is not as good as you want it to be. It also gives time for the heat to reduce and even out through the piece of glass.
As you become experienced you will find a pace that suits the kind of bead on the joint that you want to achieve. If the seam is too flat, slow your pace or increase the rate at which add the solder to the iron. If the seam has too big a bead, increase your pace or reduce the rate at which you feed the solder. It is also possible to consider other methods of soldering.
You also need consider the usual problems relating to cleanliness and insufficient flux. Sometimes the soldering iron is not hot enough, but you should notice this early as the solder will not be melting at its usual rate and will be grainy in appearance.