Errors and Mistakes

[Viladin]

In addition there doesn't seem to be any limit to the number of bombs per day a chemist can make. Not sure if that was intentional or not.

Intent. Since they don't have the Mutations like a normal Alchemist.

This seems a bit overpowered. Do the bombs have to be concocted on the battlefield or else they go inert or something? If not, what's stopping a character from making 20+ bombs before a battle and just throwing them around like a madman?

There is nothing stopping them from doing just that. Its a supernatural ability to concoct these bombs, therefore, they only get one attack with it.

Its a little high for the start, but Blue Mage spells are usually higher, plus compared to Burning Hands PF, at max damage, is less than that and only affects one person.