Was it faster than earlier methods?
Mercuric nitrate was used specifically in the felting process of hats. In order to remove the hair from the hides and have it properly "felt" together, soaking in chemical compounds was necessary. The process was called carroting because it's solution was orange, and that is what contained the mercury. This is a danger to both the people felting the fur as well as later steps because most shaping of hats requires them to be reheated while wet, releasing dangerous vapors during both processes.
This particular method spread from France in the 17th century, but you won't find many (or any) references to the issues of madness until the mid-19th century in most places (St. Petersburg first mentions it in 1829, but others not until the 1860s). That's because of all the industrial changes taking place. The dangers of mercury were known from the beginning, so most places that worked with felting built on the outskirts of cities with lots of good air movement to avoid issues from the fumes. As cities expanded and the safety of workers lost importance these structures were swallowed up and the fumes were not ventilated properly. Though there was an understanding of the danger of mercury poisoning, other health issues were of larger concern to the hatter community and took on much of the blame for ill health, such as tuberculosis and alcoholism. It wasn't until mercury was needed for war efforts that hydrogen peroxide eventually replaced it, post-WWII. Up until that point it was just another safety hazard, America even had no laws about trying to prevent it (France did in 1898), so it was better for business to ignore the issue. It's really only so prominent and well-known today because of the Lewis Carroll series, otherwise it'd be just one of many, many health issues coming out of 19th century industry.