I broke one in the kettle a few months back. Modern thermometers aren't mercury, or rather probably aren't, so you're good. Google the make/ model of the thermo and check it out. Also, I wouldn't worry about the shot at the bottom. Never checked to see if mine was filled with steel or lead, but as somebody else said you could use a magnet to check. I doubt they would be stainless steel.
Did the entire unit break apart, or just a hole in the bottom? When mine went, only the bulb at the very bottom holding the shot broke. I think the "mercury" is in an independent tube within the outer shell, anyway. Kyle
edit: as kilted said, there are probably still going to be glass shards in the beer. However, leave a little bit of wort in the kettle. When you rack off of yeast, leave the trub behind. If you keg, there'll still be trub in the bottom of that vessel. The glass will be the first thing to settle out of suspension (well, the shot first I guess) so it'll be covered by the trub. Zero concern here.