A few notes
Caveat Scisor: If you're doing this with butcher scraps as I am, remember that you're handling a non-sterile bacterial culture medium. It may have been in a butcher's trash can all morning. You should assume that it is practically alive with microbes at this point. Wear gloves. Avoid cross-contamination. If you was these pots in the same dishwasher you use for regular pots and pans, make sure you set it on "sterilize" when you wash these pots. Most dishwashers in the US have a setting that gets the temperature over 200F. Use it. If you have antibacterial soap, use it to wash your hands afterwards. That sort of thing. The last thing you want is to get sick from handling the raw (literally) materials.
This is a perfectly safe operation, provided you take precautions and use common sense.
Safety Tip: I probably should have said this earlier. Remember that this process generates steam directly from the raw materials, since there is water in the meat. This means that the lid on the container will have water on it when it is lifted off the pot. It would be natural to hold the lid over the pot to let the drips fall back into the pot rather than spilling onto your stove or counter. Do not do this. It can cause spatters and burns. Either let it drip on the counter (it's pretty much distilled water at this point) or keep a container nearby to catch the water drops when you lift the lid.
Terminology: Some people may (rightly) complain that I should be using the more generic term lard in place of the term tallow. Lard refers to just about any kind of rendered fat, whereas tallow can refer to a narrower category: rendered hard fat, or the rendered hard fat from around the kidneys of specific animals. Since I am not being at all specific in what kind of fat I'm rendering, it could be more correctly termed lard.
My only counterargument is weak: People searching for this process are far more likely to use "tallow" as the search term, rather than "lard", since lard is still in common usage and will return results for Crisco, Oleo, et al. In the interests of availability rather than accuracy, I will continue to drive the purists mad and use the term tallow. Mea culpa.