I think about buying an LG G3, but the brightness is a big disadvantage for me.
I want to know if is it possible to increase the brightness of this phone. (maybe LG is working on an update which includes fix for this issue?)
Yes, once your devise is rooted, you can change the brightness in the build properties with Rom Toolbox. But, be warned that if you are not familiar with this you should avoid changing build properties. If you don't know what you are doing you can really screw up your phone.