Popping ditto and different othermons into the daycare and it keeps saying they don't like each other very much
Monsters that have been on your team together will like each other better. Even if they don't like each other very much they'll still breed. It's only if "they're more interested in other pokemon" that they're incompatible.
A lot of people are guessing that the Shiny rate was increased.
People ALWAYS say that. It never changes, its just when theres a rush of 3 million people playing the game simultaneously and reporting in, that 1 in 8000 chance of finding a shiny is suddenly super easy to achieve among the masses.