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Okay, so the relevant text of Bracers of Falcon's Aim is as follows:
You gain a +3 competence bonus on Perception checks, a +1 competence bonus on ranged attacks, and the critical multiplier for your bows and crossbows becomes 19-20/x3.
This effect does not stack with any other effect that expands the threat range of a weapon, such as the Improved Critical feat or a keen weapon.
The bold text is what I want to ask about. These items state that they don't stack with things that increase crit range, but they do nothing to the crit range of the crossbow, so they're not expanding the critical threat range of the weapon.
In this effect, there's no reason it shouldn't work with Improved Critical.
Also are there any rules on increasing crit multiplier stacking, since the only rules I've seen for this have been about threat range, since the Bolt Ace Archetype simply provides an increase to crit multiplier, and should easily stack with this, in the end resulting with an (amazing) 17-20 x4 weapon for a light crossbow.

mplindustries |

It explicitly states that the effect does not stack with any other effect that expands the threat range of the weapon.
Improved Critical expands the threat range, so Falcon's Aim does not stack with it.
It'd be no different than if you had a belt that gave +2 to Strength that then specified it did not stack with size changes. You would get a size change or +2 to Strength.
With regards to Falcon's Aim and Improved Critical, you could have a Crossbow with a 19-20/x3 crit, or a 17-20/x2 crit, but not both.
On the other hand, it does not appear to care about critical multipliers, so those should all stack. With that Bolt Ace ability, Falcon's Aim, and Improved Crit, you'd have a 17-20/x3 crossbow, or a 19-20/x4 crossbow, but not a 17-20/x4 crossbow.
If you chose Improved crit, you also wouldn't get the bonus to Perception or ranged attacks, by the way.
To make it more clear, distill the language:
This effect does not stack with any other effect that expands the threat range of a weapon.
[X] does not stack with any other effect that [Y]
[X] (or) [Y]
You have to choose between the entire effect of Falcon's Aim or the entire effect of Improved Critical.