Few exercises are truly off-limits . There is an assumption that older people should stick to the foo-foo stuff and forgo free weights or challenging compound exercises such as squats. While it's true that the older trainee might need to work on building the skills, strength, and stability necessary for performing some exercises, this should not mean that these exercises are contraindicated. It just means that they'll take a little longer to get to. In addition, moderating the weight can be done just as easily with free weights.
Muscles learn by doing .
If you need to learn balance, do exercises that help you develop it, not exercises that allow you to do without it. Compound free weight exercises force the body to function as an integrated system. You don't learn stability by doing machine exercises that provide the stability for you. That being said, older trainees will likely have to make allowances for beginning a program with reduced stability and balance, and gradually increase the level of difficulty in their exercise choice. Working through a full ROM develops strength in all positions, and is the greatest defense against injury.