It interesting to note the alchemist, like all the spellcasting classes presented from the advanced players guide except the oracle. use a bardlike spellcasting progression - more spells known, fewer times per day, and a lower maximum spell level (with a number of spells having a lower effective level for the new class) as compared to the core classes. is this a pattern that the developers are moving towards?
To specific points, the alchemist has some strengths (I like the bombs) and weaknesses (infusion being almost required as a discovery, and the slow progression of the discoveries).
I tend to agree with kerian that discoveries should be faster paces in acquisition. Either that or you make some discoveries into feats that the player can take to augment discoveries they have already taken. That would be more balanced to what I see, allowing a player to just make discoveries and have X level of power, or augment discoveries with feats to have X+ level of power.
One thing i do like is that the Alchemist has, to me, some core similarities to the Artificer class from 3.5 Eberron. or, at least, it can. The class can take on that role if you are trying to modify pathfinder classes for Eberron use (which I may be) as the 'item maker'. Maybe some alteration to the class could be made to allow for 'off camera' potion making thats easier for this class, to offset some of the slower discovery rates? (unless I missed something in the class itself that already accounts for this)