I see these points come up a lot on the boards, so I figured I'd repost them all in one place.

1. Shield Mitigation continues after shields are down, this is explained in the manual.

2. You can add time acceleration in single player games with the + and - keys, from 1x to 8x (added in 1.02)

3. Turrets are excellent at keeping the AI at bay. The AI also fears capital ships.

4. Pirates lack shields, and should be focus fired upon whenever possible.

5. Armor is not a straight damage reduction but is effectively a 5% bonus to health per armor point. This is different than health upgrades because armor effectively makes heals and regeneration count for more.

6. Capital ships can single handedly max out the mitigation of enemy ships.

7. Fighters/Bombers without a host ship will lose health at a constant rate.

8. The computer tends to keep a large amount of credits on hand, it is not cheating when it matches your bounty of 6,000 credits on it. (except that it can do it instantly, but it's a minor issue)

9. The current system of ship maintenace being based on your current maximum is intended, it's designed so that you need a solid economic base to keep up fleet expansion, not that you upgrade as soon as you have enough money to do it.

10. Capital ships are somewhat strong by themselves, but adding a support fleet greatly increases their power.

11. Culture Buildings in the same system stack without diminishing returns, as do trade ports.

12. If you try to play a large FFA without locking the teams, you will likely get overwhelmed.

13. Building a culture building in friendly territory increases your base gather rate for all resources in that system and likely surrounding systems, because it will raise the allegiance a static 10% above it's base value. (100% -> 110%, 65% -> 75%, 25% -> 35%, etc.) .

14. Capital ships push back culture, if your culture cannot penetrate (but is not pushed back), chances are they have a lot of capital ships in that territory.

15. Pirate Strength is Increased when there are :  More occupied planets,  More cargo ships,  Higher bounties placed.  The strength is reflected on the bounty screen.

Edit 1: #13 clarified.
Edit 2: Added #15