This thread is supposed to help identifying and avoiding common pitfalls and oversight - both those you noticed in your own gameplay and those you inferred from other posts. It would be nice if we ended up with a comprehensive list.
1.) Six gunpoints.
Firing the same guns from a 4-gun bank and a 2-gun bank simultaneously results in the same damage per second as firing from the 4-gun points only. Not necessarily a mistake for those who like to snipe instead of spraying fire, but something to keep in mind.
2.) Underestimating power output.
50% more power means 50% faster recharge for both shields and weapons. Assuming same desired energy available for weapons and default settings for the weaker craft, this translates into twice the rate of shield regeneration - a useful benefit in extended fights.
3.) Picking the wrong equipment for AI pilots.
Often, bombers can do admirable anti-fighters duties serving as gunships covering one another. This also slows down enemy fighters, making it easier when flying a space superiority fighter oneself. Also, AI pilots are surprisingly competent with fighter suppression missiles.
Generally, light fighters are more survivable in the hands of the AI. If there's little time pressure but one's allies suffer from a higher attrition rate, check whether they are flying assault fighters when lighter craft would do.
4.) Engaging Shivans on even terms.
a) The concentrated firing arcs make most Shivan capitals a terror in a shootout with GTVA equivalents, but a few Trebuchets/Stilettos can often neuter either anti-fighter or anti-capital capability.
b) Thanks to better shielding and manoeverability, Shivan fighters take a long time to kill in a dogfight. However, their paper-thin hulls make them easy pickings for anti-fighter beams so it often pays to lure them near a friendly capital ship.