Advance the storyline in mission. Don't just have the command briefings explain what's happening. Integrating them into the actual missions makes the player feel as if he's actually taking part in events, rather than on the sidelines watching.
Throw surprises at the player. That's something I believe the main FS2 campaign excelled at. When you first hear about Bosch's Etak project, you undoubtedly assumed that it was some sort of weapon. In the briefings, that notion is reinforced, when the officers repeatedly say it is "probably a weapon of mass destruction". I mean, what else would a villain be constructing anyway? It then comes as a much bigger surprise when it's revealed to actually be a communications device.
People often comment that the Bosch monologues were all boring. I've always found the second one quite entertaining. How often do you see the evil guy denigrating all his men as an "army of stupid cattle"? It's the little pieces that combine to form a great story.
