The Apple Watch doesn't have many mechanical issues, since it has very few moving parts to begin with. However, the digital crown is one part in particular that can get stuck or feel sticky, making it difficult to spin. Here's how to fix that.
A stubborn digital crown is likely to get that way due to long-term exposure to dust, dirt and other grime. This gunk slowly makes its way into the cracks, and interferes with the spinning mechanism. Fortunately, it's pretty easy to clean and only takes a couple of minutes at most.
To prepare your Apple Watch for cleaning and fixing the digital crown, you first need to shut it down and remove the watch band, since we'll be introducing water into the mix. If you have a sport band, you can leave it on, since the fluoroelastomer is impervious to water---unlike leather, nylon, and other watch band materials.
You might be wary about water getting near your Apple Watch, but even the earliest models can handle it. While recent Apple Watch models are "swimproof," the first-generation model is still "splashproof," meaning you can splash a good amount of water on it and it'll be fine. In fact, even Apple recommends running water over the watch to fix this problem.
When your Apple Watch is ready for its bath, find the nearest water faucet and turn it on so that there's a slow, steady stream of warm water. You don't need to go overkill with a Niagara Falls-like stream---you want just enough water to adequately wash out the gunk that's trapped inside of the digital crown. The warm water helps break that gunk up so that it comes out more easily.
When you're ready, lower your Apple Watch under the stream, focusing on running the water right over the digital crown.
As you do this, turn the digital crown wheel multiple times in both directions to loosen up the gunk and wash it out. Do this for about 15-20 seconds.
Dry off the watch (ideally with something that's non-abrasive) and give the digital crown a spin. It should feel like new and turn more easily now. If not, dunk it in water again and repeat the steps above until the crown stops feeling stuck or sticky.