I am wondering what would it improve to add 2 more slots to my bridge officers?

You can have two more bridge officers join your crew?

Having more bridge officers is great, because it allows you to train them differently depending on ship or even situation. E.g. you can switch from "beam cruiser tac boff" to "cannon escort tac boff" or from "offensive cruiser setup" to "team healing cruiser setup" without having to retrain skills every time.

It also helps immensely when you swap between two different ships.
For example, having additional boffs means I do not have to re-train when I transfer from my heal/tank cruiser to a dps escort/BoP.

It can also give you more tactical choices, even with a single ship... Within a single mission with my cruiser, I can switch from 'Beams Fire at Will' & 'Torpedo Spread' for mob control, to 'Beam Overload' & 'Torpedo High Yield' to maxmize damage to a single target.... For Defense, I could switch from 2 'Transfer Shield Strength' for shield tanking vs. 'Hazard Emitters' & 'Polarize Hull' for anti-Borg work...

After a while you learn the tricks of different enemies.

On my Tactical especially the few engineering and science abilities I have are great to be easily switched - sometimes Science Team is more helpful then Hazard Emitters even, if the enemy "shoots" with debuffs rather then plasma weapons.

I believe I have 14 BO slots on most of my characters, and most of those are filled. And in addition to what was said above, it also allows you to accept BOs for training purposes, like if you are a tac and training Rapid Fire 3 for someone.

If you can get them trained in Specific abilities, you can tailor your away teams to what you are fighting.

Yep....different Boffs for different ships.

I have one "Space Team" and one "Ground Away team"

same here, my ground team usually have passive traits that will help them out. I usually shop around until i find one with a high % trait of what i am looking for. For example one passive 5% chance to exploit is pretty common, but i keep looking until i find one that has 15% chance to exploit, and another 5% chance to exploit from another trait.