I've had problems with slugs early, but surrounded them with egg shells and that seemed to help. I've got four courgette plants growing and they are fruiting madly. They are pretty thirsty plants and I water them every day, sometimes twice a day when it is really hot, and feed them once a week. That seems to work.
Oh, I don't know if anyone else finds this, but I have found that my courgettes grow better in pots than in the ground. I planted one in the ground this year and it is not as far on as those in pots and not cropping as well either.
If the small courgettes fall off instead of developing it is because they have not been fertilized.