Are Mercury-containing silver fillings dangerous? Should I have my old ones removed and replaced?

Easy answers: NO and NO, but read the long answer!

Long answer: Mercury-containing silver fillings are known as “amalgam” fillings. They are an amalgam, or mixture, of several metals mixed in proper ratios to create a hard, durable, and long-lasting filling material. The metal in highest concentration is silver, while mercury provides the “liquid” portion of the mix.
Methyl Mercury, or “quicksilver”, in its pure form is toxic. But when mixed, or amalgamated, with the other metals in the proper amounts, it becomes non-toxic. Once the metal hardens, there is negligible if any risk. There is more mercury vapor from industry in the air we breathe than there is from a set filling.
A great example is the chemical chlorine. If I give you a glass of liquid chlorine, like Clorox, and you drink it, we will all be attending your funeral. But if you mix that same pure chlorine with the chemical sodium in the proper ratios and conditions, you have Sodium Chloride – table salt. A relatively non-toxic item.
Silver fillings are no longer the filling-of-choice, and have not been for many years. But silver fillings have been around for decades, and we routinely see 20, 30, 40 year old fillings. Some of these fillings are still doing their jobs. And some of these fillings are no longer well sealed, or are breaking down, and need to be replaced. And bonded, tooth-colored composite resins have more advantages, probably fewer long-term drawbacks, and of course look a lot nicer. These bonded composite fillings are now one of the materials-of-choice when a filling is the treatment you need.
As far as removing and replacing old fillings: Any time you work on a tooth, you irritate that tooth. It is believed that irritation to a tooth is cumulative, and enough irritation can cause the living tissue in the tooth to die. And there is no way to measure and truly know the level of irritation a tooth has endured. So unless the benefits of replacing the filling clearly outweigh the negatives, you do not need to replace your old fillings before their time. At your request, we will gladly replace your old silver fillings with beautiful tooth-colored fillings, but only after you understand the pros and cons. And when they do require replacement, tooth-colored fillings are a great option.