For the discoveries for alchemist, a good chunk of them say "An alchemist must be at least X level before selecting this discovery".
Case in point:
Explosive Missile: As a standard action, the alchemist can infuse a single arrow, crossbow bolt, or one-handed firearm bullet with the power of his bomb, load the ammunition, and shoot the ranged weapon. He must be proficient with the weapon in order to accomplish this. When the infused ammunition hits its target, it deals damage normally and detonates as if the alchemist had thrown the bomb at the target. If the explosive missile misses, it does not detonate. An alchemist must be at least 4th level before selecting this discovery.
Does this refer to character level or to class level? AKA a character who is 3 Barbarian(or any other class really)/2 Alchemist has a character level of 5 but only an Alchemist level of 2 (which some discoveries are based off of Alchemist level explicitly like Spontaneous Healing)