Okay, to start with a disclaimer:
I am head over heels in love with the premise of this class. I want it to work out well more than any class that Paizo has released so far.
That all said there are some issues that stand out to me as problematic.
Firearms rules: While I think the firearms rules, including ammunition prices make a sort of sense for firearms when used by individuals other than gunslingers, they start to break down when you have a character who is dependant on them. Obviously, these rules are not changing so perhapes adding abilities that let the gunslinger break some of the rules.
Any gun slinger is going to burn through their wealth in no time. As such might I suggest that Grit be altered to allow gunslingers to shoot more often, without completely negating ammunition. So long as the gunslinger has atleast one point of grit, he doesn't expend powder or bullets when using his firearms.
This way he can shoot round after round, but if he runs out of grit, he starts using up ammo quickly and at great cost.
Damage and reload speed
While I don't think this is as bad as some of the optimisers are making out, there is an issue. Guns give up a lot, and while the ranged touch attack is awesome and does help, composite long bows are still cheaper and better. Again, the rules for firearms are already settled, so I would suggest a class feature that allowed the gunslinger to add damage to each attack equal to his current grit points. This means in general that he will start of hitting hard, but slowly loose strength as the day goes on.
Additionally feats that allow faster reloads and or, weapons with highter rate(or two barrels for manyshot) will almost certainly be needed later on.
Deadly aim
While I know it has been mentioned before, I would like to suggest that the feat deadly be altered to allow it to work with pistols.
Daring acts
As it stands, if your skillful, your chance of gaining from a daring act is actually lower than if your terrible. I would suggest that either, you go with a mechanical approach that rewards skill(such as when you beat the DC by ten or more) or creative flair, by making Daring Act a class feature in its own right. Such a class feature could work in a similiar manner to Stunts from Exalted, providing mechanical rewards such as grit for engaging descriptions.
In short, I would like to see grit yo yo throughout the day, as the gunslingers player burns it away, then does cool and dangerous stuff to earn it back.
Other Deeds I love the deed, but the list is narrow. I know well get more in the finished book. I think several fairly quintessential we could get a swift action self heal, or temp hitpoint generating Deed, so that the gunslinger can limp on after walking across broken glass and taking a beating, that would be great, as would some sort of intimidation deed, and a Immediate action snapshot style deed.
Prestige: Last of all, i would love you all forever, if in the final book, we saw a gunsinger prestige class with 'scene editing powers' that use grit as fuel.
DM: 'Four hellknights burst into the room, theirswords glowing with malign energy.'
Gunslinger: Damn it, I turn on my heel and start to run. Behind me the Hellknights start to give chase. The leader howevermisplaced his foot and the rotten floor gives way under the weight of his armour. Sucks to be him.
DM: Cool, you make it to the corridor, it looks like there is only one way out, which is through the other patrol.
Gunslinger: I twist the other way, running the other way, at the end of the corridor, throwing my self through the window with abandon, only to land two stories below on barge filled with raw cotton.
DM: The hellknights shout and wave their fist in rage as the barge slowly moves of down the cannal. You have bought your self time, but those hellknights will be on you trail again soon, better find your comrades quickly.