1. Weapons jamming in a fight. You in a desperate fight, trying to activate every buff, then your cannon rapid fire jams, you weapon stops firing and you have to wait 30 or so seconds before you can start firing again.
2. Projectile weapons misfiring and being put on cooldown.
3. After dying your ship turns invisible. You're still targetable of course, but you can't see your ship. Makes it rather hard to align you DHCs
4. Scramble sensors causing evasive to fail.
5. Beaming back into a map and finding you're stuck in a console.
I think this is thread isn't meant to be a "Post your top 5 annoying bugs", it's only the personal top 5 of the opener.
For your 5) the command "/stuck" helps on some maps. Simply enter it into the chat.
Now back to the topic: I think, if the opener says he uses beams on the Vesta, then the advice "Use 3 Aux-DHCs in front" is fail. My scientist has got also a Vesta and uses Romulan-Plasma Beams and Dual Beams. I can still use the built-in subsystem-targeting and Beam-abilities like Fire at Will.
I also use the Romulan Hyper-Plasma-Torpedo-Launcher in front and the Omega Torpedo-Launcher in the back.
Finally I've got also the Cutting-Beam mounted on the Vesta.
That's the reason why I run weapons at 121 Power - anything above 125 would be just a waste.
If Star Trek Online was an Open-Source (GPL) Game, we would have a low-grind fork.