how warfarin killed rats (and other rodents, too) is to "thin" the blood so much that they spontaneously bleed to death internally. They had to have massive (comparably, weight for weight) to do this. So, the small doses that we are subject to, and the monitoring that we get, should prevent this rather nasty "side effect". As to the long-term effects on other major organs, my own personal attitude is that I will deal with it if it happens - I have just been given 2 years of life so far that I wouldn't have had if I hadn't had the valve replaced.
I know where you are coming from with your question, I am on other meds long-term, and when I asked that doc about the long-term effects, he was aghast and questioned iif I was thinking of stopping them. I explained that I wasn't, but that I went for annual physicals, and my PCP and I would just throw in a few extra kidney function tests if kidney problems were a known side effect, and that we would both know what to watch out for in the future.