Probably my main piece of advise for us older riders is to mix it up. It's important to have other athletic interests. I use hiking, weights, and rock climbing in addition to road biking. If I get too obsessed with any one of these, I start to hurt. Changing activities is a good way to take a "rest" day, although there are times I take a real rest day, too. I have friends my age (almost 61) who are interested in only one activity, and they seem to be dealing with an injury most of the time. A regular stretching routine also makes me feel better.
It is especially dangerous for an older person who has not been active at all, and suddenly decides to "get in shape", so he/she abruptly jumps in with an intense schedule of biking or any other active sport. That's an injury waiting to happen. Even though I had been very active my whole life, I found this out when I started a new sport, technical rock climbing, at age 45. Within about a year, I got shoulder tendinitis that took 8 months to heal, and then only with the help of a cortisone shot. In the winter, that shoulder still stiffens up, and it appears I'll be dealing with it for life.
There are books out there for older athletes that are worth reading. I've found a few. "Cycling Past 50" has important info, and I'm sure there are others.