It's not fair to criticise sixties television for its poor special effects, but it is reasonable to ask whether they base their attempts on a sensible mental model of what space combat could look like. In the case of Star Trek, as the visual effects get better and better at representing their mental model, it becomes more and more apparent that the answer is no; astrogation in the Star Trek Universe is riddled with peculiar assumptions. However, my complaint here isn't primarily that ST:TNG visual effects are an insult to our intelligence; it's that greater realism, applied in moderation, would make them so much more exciting and imaginatively appealing.
Star Trek vessels are well lit in the depths of interstellar space, as are the nightsides of the planets they audibly whoosh by; meanwhile phaser beams, tractors et cetera appear as glowing lines, despite the lack of air to scatter the light. I trust you recognise this as “artistic licence” – though ST:TMP1's underlit ships were an aesthetic improvement. But do you ever wonder how anyone spots Klingons approaching at a hundred times the speed of light? Forget mere Doppler effects; the image should arrive time‐reversed, after they do! So who needs cloaking devices? Faster‐Than‐Light vision must be standard in the Star Trek Universe; as in “Tin Man” (ST:TNG3), when they watch a nova three and a half light‐hours away.
Maybe the best available rationalisation is that both the viewscreen shots and the somewhat mysterious “external views” show scenes as viewed not by human eyes, but by radarlike subspace‐sensors; which would also help to explain how Spock can always tell that “we are being scanned”.
What exactly are those diverging “stars” that the USS Enterprise is always flying through? If they're really stars, this implies speeds of a million‐plus times lightspeed; yet they keep zooming past even (e.g.) in “The Galileo Seven” (ST:TOS1) when the Enterprise is in a parking orbit… Well, maybe they're hydrogen molecules, or some subspatial equivalent.
Next consider the speeds and distances entailed in intersystem travel. In general, if you can see one another, then you're flying dangerously close. Nevertheless, we commonly see starships sitting nose‐to‐nose, practically immobile relative to one another (even whilst accelerating under warpdrive; as for instance in “The Survivors”, ST:TNG3). Maybe these views are computer‐enhanced, and largely conventionalised to suit human psychological needs? Let us pretend so; I will hypothesise furthermore that the “stars” are added as a false‐texture speed indicator by their Viewscreen Computers. Similarly the atmospheric sound effects.
Then there's combat. Fights can occur at warp eight (“Journey to Babel”, ST:TOS2), but nobody exploits manoeuvres like the Dewarp and Backstab Your Pursuers tactic or has trouble with the ranges during head‐on charges. FASA's Star Trek wargame simply outlaws warp factor changes, treating it as if it were all slower‐than‐light; a blatant cop‐out. Note (“Balance of Terror”, ST:TOS1) that plasma bolts, phaser beams, and so on move much faster than starships, while the beam of a hand phaser is so slow you can see it move! We must assume ships' phasers are souped up with some kind of extra subspace field, which may explain their visibility in scanners.
All movement in the Star Trek Universe is two‐dimensional. Starships, including newly met aliens, only operate on the plane, never exhibiting pitch, roll, or yaw, let alone diving or climbing. Everyone agrees which way is “down” (Borg vessels fly the same way up as the NCC1701D), and goes into orbit round planets at similar odd angles. Moreover, motion is not only pre‐Einsteinian, but Aristotelian! Drives producing constant thrust induce a constant velocity, not acceleration, so you can do warp‐9.8 hairpin turns without slowing down (“Encounter at Farpoint”, ST:TNG0); but if you are power‐drained like the shuttles in “The Voyage Home” (ST:TMP4) you swiftly coast to a halt.
The paradigm is one of roughly World‐War‑I‐style naval warfare, with ships limited to two‐dee movement through a resisting medium. Cloaked vessels are metaphorical submarines; “The Wrath of Khan” (ST:TMP2) adds one solitary “submerge‐and‐resurface” tactic (and boasts of this “three‐dee thinking”); while ST:TNG tries to make its manoeuvring look a little more flexible. But none of this rises to the level of Battlestar Galactica's World War II aircraft‐carrier warfare metaphor, or Star Wars' aerial dogfight paradigm, let alone treating all three dimensions as equally useful, and no particular direction as “down”. Is it too late to start imperceptibly phasing in this kind of imagery?