Very helpful thread, thank you for the tips!
One tip I can add, along the lines of checking and cleaning your lens. If your phone has a screen protector, make sure it's not obscuring the lens. I got a new screen protector for my phone - a thin glass one, as opposed to the clear plastic I used to get - and the opening cut into it for the selfie camera was a little too tight around the lens - it was about exactly the size of the lens, no leeway. So the edges of the hole were creating a halo effect on the photos that took me FOREVER to figure out! I kept cleaning and cleaning and blowing on it, but couldn't get rid of the damn halo. The hole was collecting dust and stuff around the inside edges, too. Now I need to look for a new screen protector - one that leaves more room around the lens.
My dSLR's focus broke a few years ago, and I haven't been able to justify replacing it yet (those things are expensive!) So I'm very sad that I'm stuck with just a phone camera for now. Even with the dSLR though, I always hated photographing children and animals, because they never stop moving! You need to have the perfect light conditions to get a clear shot of a moving target, otherwise they come out out of focus. My phone's camera is much better at handling low light without long exposures, and preserving (most of) the sharpness of the image. Not as good as a real camera, but the real camera fails miserably under these non-ideal conditions, so... the phone wins.