That's not a problem; that's nature at work A healthy lawn has lots of worms working away underground taking nutrients down into the soil and aerating the soil, helping to keep the roots healthy and at this time of year, when we have heavy rain the worms are working even harder. Sweeping them with a besom is the traditional way to deal with them. Raising the height that you cut the grass in the autumn means that the grass will hide them a bit better.
I'm afraid that we all have to get used to the fact that a real lawn doesn't look like astroturf.
As for the mushrooms - they're another of Mother Nature's glorious products - you can either do what I do and enjoy their shortlived beauty and wonder at the great underground network that makes up the rest of these amazing 'plants', or scoop them up and put them in the bin.
Unless they're Shaggy Ink Caps or one of the other easily identifiable edible ones, in which case I'll pop round and cook us up a meal of bacon, egg and mushrooms