Does targeting the bridge and engines of capital ships do anything?

Solution 1:

Yes! They are a pain to take out, but when you do, you will likely complete a bonus mission (all of the ones I've managed to blow up so far have) in addition to providing a nice chunk of XP. The bottom of first cartel listening station for example will give you 500 points for the kill and just under 3000 for completing the bonus mission. I try to save my missiles for those items in particular since they are definitely hardened targets.

Edit for additional info: The space stations and capital ship bridges I have destroyed so far have been bonus missions all by themselves with no other targets. Blow them up and you instantly get both the base experience and the bonus mission experience. There can certainly be multiple bonus missions per encounter. One listening station had the fighter ships, the communications relay (the hard point at the bottom), as well as satellites plus turrets. Essentially, if you can target it, it CAN be blow up. I try to blow up everything I can, and make a mental note of what triggers a bonus mission. I haven't come across a good guide to all of the bonuses yet. Only one way to find out - blow up ALL the things!

Solution 2:

On the crippled destroyer missions, obliterating the bridge of the main capital ship awards:

• Sarapin Assault (Imperial)
  • Eliminate the Enemy Command, 2538 credits, 2970 XP (@ 25)
• Makem Te Assault (Republic)
  • ?

Destroying the target at the bottom of the space station awards:

• Cartel Listening Station (Imperial)
  • Cripple Republic Communications, 2538 credits, 2970 XP (@ 25)
• Balosar Outpost (Republic)
  • Take Out the Communication Array(?)