Can you leave silver fillings in your mouth
...without doing harm to yourself, others, or the environment?
Apart from the "amalgam" lobby who will swear on their grandmother's head that mercury and other serious toxins in dental amalgams are safe (after all, they have been used for 150+ years), interestingly, at least two alternative "dental" authors I know of maintain that as long as nutrition and/or health status is good, amalgam fillings can be tolerated.
Likely, this will also depend on the ability of each individual to detoxify mercury. Apart from the frequently crucial dietary and lifestyle (compare below Addendum) factors, another determinant of such mercury detoxification ability seems to be genetic, with a certain genotype, the AP01, possessing two cysteine amino acids which protects you from mercury (and the mercury-related disease Alzheimer's).
If you happen to be a AP04 genotype, the AP04 gene you carry possesses two arginine amino acids which does not protect you from mercury and hence predisposes you to developing Alzheimer's.
There are two intermediate genotypes, the AP02 and AP03, which carry one cysteine and one arginine amino acid; carriers of these genes do develop Alzheimer's, but to a lesser degree than the AP04 genotype.
So yes, tolerance to amalgam fillings as long as health status is good may well have a measure of truth on a purely personal level (also compare Are all amalgam carriers "doomed"?. But the following deserves consideration as well.
Antibiotics resistance due to mercury
Until recently, it was assumed that the only thing that makes bacteria resistant to antibiotics was repeated administration of antibiotics (such as penicillin). Once the bacteria living in a person's body have become resistant to penicillin, they secrete so-called plasmids (small bubbles containing a piece of DNS or RNS, teaching the other bacteria in the environment how to become resistant to penicillin).
In a person carrying amalgam fillings, the oral bacteria (which also live in other parts of the body such as the intestines and the blood) become resistant to mercury, copper and the other metals contained in the mouth and simultaneously, become resistant to all antibiotics. In other words, bacteria which normally colonize our body will live in us happily ever after but won't respond to any antibiotic therapies.
And more than that - each time we breathe out, we send millions of plasmids into our environment, teaching other bacteria how to also become resistant. In addition, at each outbreath (at least when speaking, coughing or yawning), we send mercury vapour into our surroundings.
Conclusion: keeping or removing amalgams?
So personally I certainly wouldn't advise keeping any amalgam fillings (but see the important qualifications in the following paragraph). For an enumeration of many serious reasons, see for instance the detailed information found in the article On the dangers of dental amalgam (mercury) "silver" fillings (including for the environment) and Dr. Dietrich Klinghardt on the dental toxicity issue.
A pithy quote is owed to Dr. Hildegard Schreiber MD (a German public health official specialised in microbiology and the epidemiology of infectious diseases) who wrote about people carrying amalgam fillings, "During mastication, up to ... 700µg of mercury are released... if saliva were drinking water, one wouldn't be allowed to swallow it (translated by Healing Teeth Naturally)."
Ironically, not everyone gets better (in fact, the opposite can happen, with symptoms getting worse) after having their mercury fillings removed. Several of the possible reasons (particularly improper removal of the fillings) can be found under The importance of safely removing (mercury) amalgam "silver" fillings.
Addendum - on the role of sunlight
If we can transfer the results of animal experimentation to humans, we can help our bodies better deal with toxins including mercury by exposing ourselves to sunlight. See Sunlight - the ultimate detoxifier?.
2 This information is owed to the book Toxic Dentistry Exposed by Drs. Munro-Hall, see Books.