Something that I don't understand (from a technical point of view, that is; I can understand why this isn't the case from a story-telling point of view) is why, during close combat, starships don't utilize a method of destroying the enemy's torpedoes the instant they launch, in unshielded ships, or when they reach the perimeter of the firing ship's shields.
According to the tech manuals, sensor systems and computers work at FTL speeds. Almost as soon as the weapons officer on the threat ship presses the button to launch the torpedo and the torpedo begins to move one meter down the tube, the sensors on the target ship should detect the increase in power and movement in the weapons systems and an automatic command should be given to the phasers to target the threat ship's torpedo tube if unshielded, or a wide-area effect directed towards the portion of the threat ship's shield envelope that the torpedo is likely to pass through on its way towards the target ship. From a tech standpoint, there's no reason why as soon as the threat ship's torpedo leaves the tube, there shouldn't be a phaser strike inbound and timed to detonate the torpedo just as it departs the threat ship's tube, or shield envelope.
Additionally, while watching some of the big battle scenes towards the end of DS9's run, it seems like no one is using shields; I see phaser/disruptor/polaron beam impacts and torpedo hits against ship hulls directly, with no shields. Was it ever explained what technology was used, or by who, to cause shields not to function? Or was it just a decision by the VFX people to not use shields?