Staying strong at 60 and beyond is a very important component in your quest to enjoy your current lifestyle and set yourself up for an enjoyable and active retirement. If you're looking to have more energy, improved immune response, handle stress better and keep your bone density higher to better protect you, you'll need to focus on building your strength. It's not hard to do, but you'll need to train differently than you would to build muscle size.
Lifting a weight that's too heavy for you is an error despite the part of the body you're working, however it can be really disastrous when performing shoulder workouts. The shoulders are complex and delicate joints that are not specifically simple to target, and if you do put them under excessive pressure before they're ready you can wind up with injuries that put you out of action for months.