Depending on what's in your water, you may get some mineral build up eventually. Some people report staining from potting soil, usually this seems to get blamed on peat moss in the mix. I've never seen it happen myself. On the other hand, I nearly always use saucers, and water carefully with an eye to NOT overrunning the saucer - so anything like that would be kept inside the saucer.

I usually use saucers because it's neater when watering. I feel like (with no basis in peer-reviewed research) keeping the water where the plant is is less wasteful, especially now that I've moved to a desert clime. Because it can soak the rest up during the day. Or it evaporates off during the day and provides a teeny bit of extra humidity - but then this is a very dry climate I'm in now. Other places I have lived were already plenty humid!

It also lets me bottom water occasionally. Saucers are usually too shallow to do any damage when bottom watering, especially in the summer.

I am shifting over to drip irrigation for everything, including in pots. One summer I had all my plants AND all my neighbor's plants - even the hanging baskets - on drip irrigation. My water bill went way down and everything grew like crazy beause it was so evenly watered. Had the whole thing on a timer. It was great.