ST weapon accuracy and range
This article will deal with demonstrated accuracy of various weapons used by major Star Trek civilizations like Federation, Borg, Dominion, Klingon Empire etc. As the examples provided below will demonstrate, all major military forces engage at ranges of several hundred meters up to several kilometers which present the upper limit of their effective weapon accuracy.
Examples
DS9 "Call to Arms"
In the episode Dominion fleet attacks Deep Space 9 and it is revealed that even when engaging a completely immobile target ST ships need to close to several kilometers before opening fire.
The screenshot on the right shows the Dominion/Cardassian fleet approaching the Deep Space 9 to the point of it taking up a significant fraction of the field of view. Yet in the following scene Damar reports that they will not be in weapons range for another minute.[1]
After the battle is joined the attacking fleet continues to fight at extremely close ranges however even ranges of several hundred meters appear to great for Deep Space 9 targeting sensors to achieve a reasonable accuracy. On the left we can see a Cardiassian shuttle flying straight towards Deep Space 9 central assembly. The shuttle doesn't change course nor does it attempt to evade the incoming fire yet Deep Space 9 misses it, or rather, scores two grazing shots thus failing to stop the craft.
Further evidence of limited accuracy comes from the end of the episode. As Defiant and a Bird of Prey flee DS9 Dominion fleet opens fire and we see 11 shots being fired yet not a single one hits the fleeing ships. The shots can bee see on the right and, as is immediately apparent, the ships are flying in a tight formation without making any attempts to evade enemy fire. As before the range is on the order of several hundred meters or several kilometers at best.
TNG "Conundrum"
Worf reportedly states that the ship's phasers have a range of 300,000 km, yet later in the episode Riker says they are still several seconds from "optimum range" for targetting the Lysian command center, even though they are practically on top of a stationary target that is both very large and very poorly defended (by Federation standards).
TNG "Yesterday's Enterprise"
Three un-cloaked Klingon Birds of Prey close to within a few kilometers before firing on the Enterprise. Likewise, the Enterprise, knowing they will be attacked by the Klingons, doesn't fire until the enemy is at close range (the Federation was in a state of war with the Klingons in this alternate-timeline episode).
VOY "Equinox"
Voyager reportedly attacks the Equinox with phasers from 30,000 km away.