The alchemist (and thrown splash weapon) rules aren't too clear, so, here's how I interpret things (see links for details, and sometimes FAQ quotes):
It's a bit unclear whether infusions of a target:self can be made to affect others. (See http://paizo.com/threads/rzs2pm2d?Self-range-spells-and-the-lack-of-a-Sawing). Until the faq is answered, they do not. Consider the following paragraph to be part of the Alchemist class description:
"Infusion: When the alchemist creates an extract, he can infuse it with an extra bit of his own magical power. The extract created now persists even after the alchemist sets it down. As long as the extract exists, it continues to occupy one of the alchemist's daily extract slots. An infused extract can be imbibed by a non-alchemist to gain its effects. Infusions that function as personal range spells still only affect the alchemist who created them.".
Alright, you convinced me, this nerf is history.
Alchemist Bomb House Nerf The second paragraph of the Bomb ability is changed to the following: Drawing the components of, creating, and throwing a bomb requires a standard action that provokes an attack of opportunity. Thrown bombs have a range of 20 feet and use the Throw Splash Weapon special attack. Bombs are considered weapons and can be selected using feats such as Point-Blank Shot and Weapon Focus. On a direct hit, an alchemist’s bomb inflicts 1d6 points of fire damage + additional damage equal to the alchemist’s Intelligence modifier. The damage of an alchemist’s bomb increases by 1d6 points at every odd-numbered alchemist level (this bonus damage is not multiplied on a critical hit or by using feats such as Vital Strike). The target of the direct hit can attempt a Reflex save (at DC 10 + 1/2 the alchemist’s level + the alchemist’s Intelligence modifier) for half damage. Splash damage from an alchemist bomb is always equal to 1/4 of the direct target unsaved damage (so if the bomb would deal 13 points of fire damage on an unsaved direct hit, its splash damage would be 3 points of fire damage.)
Alchemist Bombs (not in use yet, but any future Alchemists will use this)
Alchemist Bombs don't attack Touch AC, they attack Flat-footed AC. (AC 5 to attack an unoccupied grid intersection.)
A miss that would hit Touch AC does not scatter (unless it is a critical failure, or the miss is due to 'miss chance'), and does cause splash centered on the attacked creature.
This lowers the to-hit chance to something reasonable, making the high damage not quite so devastating.
Avoiding Alchemist Attacks
Deflect/Snatch Arrows works against alchemist bombs. As does a giant's ability to catch rocks/incoming thrown weapons. If the bomb is caught, snatched, etc, it instantly become inert rather than blowing up. If it's deflected, it hits somewhere else and blows up normally in that location. (source, source)
Pearl of Power
Doesn't work for Alchemists (or Sorcerers for that matter.)
Throwing into Melee
As long as the distance between the target and nearest friend is over 10 feet, the -4 penalty does not apply. That is, on the grid, if there are two empty squares between the targeted creature and any friendly characters who threaten (or are threatened by) the targeted creature, you're fine.
If you target an an intersection (i.e. intend to do only splash damage), consider the intersection to be the targeted creature, but note that you can't target an intersection occupied by a creature (i.e. the center intersection of a Large creature.)
Precise Bombs (new rules, the previous ones were not only complicated, but actually wrong)
If the thrower uses Precise Bombs, the excluded squares are not considered to be part of the attack (i.e. they can be used to game the rules above.)
On a miss (i.e. scatter), excluded squares are not considered to be excluded. I.e. on the grids below 'x' is the intended target, 'z' is another monster, '@' is a fellow pc, as is '$', the center square is colored orange, splash squares are colored red, excluded squares are colored blue (i.e. no squares are excluded on a miss.)
...$. ..... ..xz. ..@.. .....
And this is the result if the scatter was 'one square to the northeast'
...$. ..... ..xz.
Multiple bombs per round
Only possible through the Fast Bombs discovery.
Combining Bombs and Alchemical Items
Only possible through the Fast Bombs discovery .
Weapon Feats that work with (and only with) Fast Bombs
Fast Bombs Explained
Using a bomb is the special attack Throw Splash Weapon (Standard action), meaning that it cannot be combined with any other attacks, unless the character has Fast Bombs , which "functions just like a full-attack with a ranged weapon."
From the rules it's debatable whether it's possible to mix bombs and alchemical items, but I'll - hesitantly - allow it.
However, as it's not possible to Quickdraw alchemical items, the maximum rate of fire is one alchemical item every other round.
A character with BAB 1,Fast Bombs, no other attack modifiers and who is already holding an alchemical item can as a Throw Splash Weapon (Standard Action) with his right hand throw 1 bomb at 1-2=-1 and with his left hand 1 alchemical item at 1-2=1 on round 1, throw 1 bomb and draw 1 alchemical item on round 2, throw 1 bomb and 1 alchemical item on round 3, etc...)
If the character above also has Rapid Shot and Improved Two-Weapon Fighting he can as a Full-Round Action throw 1 bomb with his right hand at 1-2-2=-3, 1 bomb with his left hand at 1-2-2=-3, throw another bomb with his left hand at 1-5-2=-6. (In the first round, ALL the items in one hand can be exchanged for throwing ONE alchemical item, making no more than one attack with that hand as Quickdraw doesn't work on alchemical items, then alchemical items can be used every other round as above.)
If the character above has leveled up so that he now has a BAB of 6 (i.e. two attacks, one at +6, one at +1) he can, as a Full-Round Action, throw 1 bomb with his right hand at 6-2-2=+2, another bomb with his right hand at 1-2-2=-3, another bomb with his left hand at 1-2-2=-3 , and yet another bomb with his left hand at 1-5-2=-6. (The note on alchemical items above applies here also.)