Splinter shots are a sucky rule. But JD Wiker, our lovely man at the "Jedi Counseling" section of the SWRPG website, had this to say:
Q: Splinter shots, from page 54 of The New Jedi Order Sourcebook, seem completely useless. There is no benefit that my players or I can find to using them. They don't do any extra damage, and they can't damage hull points, so, as near as we can tell, they're worse than regular shots, which do the same amount of damage but can damage hull points.
A: I've actually been examining this issue recently with another player, and after much discussion, here's what we came up with: You take the splinter shots as a full-round action, as though you were making a full attack. If the splinter shots penetrate the dovin basal "shields," you can immediately switch over to full power and fire an ordinary shot -- potentially, more than one.
The number of shots it took to penetrate the dovin basal's shields determines how many "real" shots you get. If it takes more than one attack roll to penetrate the dovin basal's shields, you only get one attack at full power. If it only takes one attack roll to penetrate the dovin basal's shields, you get to make a full attack (as though you'd been doing that all along).
This system would avoid the "Why not just shoot at full power?" issue, because this way you're not wasting "real" damage on penetrating the shields. (If you can't penetrate them with splinter shots, it's a moot point anyway.) Gunners with only one attack won't particularly benefit, since their "full attack" sequence is still just one shot.
If a ship making a splinter shot attack is in pursuit of another ship, and the splinter shots get through, the pursuing ship may make a single attack as a free action, as per the usual rules for pursuit.
Here's another thing: The spot in the RCRB which says, on page 65, that characters multiclassing get only ONE of the starting feats, is INCORRECT. Multiclassing characters are supposed to receive ALL of the starting feats. Please remember to adjust your sheets on Saturday if there is anything you're missing (which is unlikely, but possible).
This was fixed in the second print run, but I don't know which you have.