In 1996, the evidence for silver as a treatment was reviewed:
It explains that silver has been promoted as a topical ointment for the treating of warts, burns and as an antiseptic. Colloidal silver has also been promoted as an "antibiotic" for ingestion.
However (as of 20 years ago), there was little evidence for its effectiveness:
Recent promotional assertions made anout the effectiveness of these products in numerous diseases remains unsubstantiated. [...] We conclude that the risk exceeds the unsubstantiated benefit for OTC silver-containing products. Consequently, there are no FDA approved CSP products available OTC.
What risk are they talking about? Well these is a more recent review of that:
The adverse effects of chronic exposure to silver are a permanent bluish-gray discoloration of the skin (argyria) or eyes (argyrosis). Most studies discuss cases of argyria and argyrosis that have resulted primarily from exposure to the soluble forms of silver. Besides argyria and argyrosis, exposure to soluble silver compounds may produce other toxic effects, including liver and kidney damage, irritation of the eyes, skin, respiratory, and intestinal tract, and changes in blood cells.