Re: black dots--hard to say without a photo.

The other looks like a slime mold in the "vomit fungus" category. Seriously. Google it. You'll see stuff that looks very similar. When it gets larger, it's less orblike and more vomit-y in appearance.

It's harmless. Fungi that cause disease are pretty organism specific. The presence of mushrooms or molds isn't in and of itself a danger to your plants. I'm guessing your growing medium has a lot of bark fines in it or something. Have you had a lot of rain lately? Normally I wouldn't ask that for LA, but your weather has been a bit wetter this year, I believe.

If you haven't had a lot of rain, you may be overwatering. In pots that size, stick your finger down into the soil an inch or two and check to see whether it's still moist down there before watering. When you do water, drench the soil really well. Water deeply less often, not shallowly more often. If the surface is never drying out, you're watering too frequently and possibly too shallowly.