What space effects, if any, do you find convincing?
Well, the point is that everybody knows what space looks like. The same way that everybody knows what sea looks like, even if one hasn't ever actually been aboard a boat or anything. The expectation is there, and just like a tempest-in-a-teapot scale model of water always utterly fails to deliver, so does a starfield that doesn't look like a starfield.
Any space effect that describes something unfamilliar to us is fair game for "being good enough" unless there are damning factors such as poor stability or focus or whatever. Every instance of the Galactic Barrier thus convinces the bejesus out of me. The Doomsday Machine is great. Balok's Fesarius is awesome.
The space in which they supposedly exist is not. That is, it's not space. And the movements of the
Enterprise, arguably an acceptable spacecraft, are not movements, but merely sorry imitations thereof.
Modern VFX can do photorealistic space (even if it's quite a bit on the dull side) and convincing movement. Nothing back then could, not even on a movie budget, but certain movies at least got significantly closer.
Between that and old-style visuals lies an uncanny valley parsecs wide. It simply fails to deliver, when every filler shot of a cop show or a cowboy series automatically succeeds (unless they try to get smart and portray movement with back projections or reality with sets, but the point is that they don't need to do that). This in turn digs another deep and wide chasm, this time between space scifi and almost all the rest. And Trek sits on the wrong side of that chasm, in the 1960s and the 1990s and basically in the 2020s still. But not all of it: modern Trek manages to slip in some shots that meet the cop show or sitcom standard of convincing, while TOS never did.
As regards the space shots, that is. To step outside the parameters of your question, many of the surface sets and associated mattes were quite effective, sometimes by virtue of being convincing, sometimes by virtue of being fantastic. But the space shots only succeed when they describe the fantastic. Which, thankfully enough, happens often in TOS...
Timo Saloniemi