I can't speak specifically for Plato, not being familiar with the manuscript tradition for his work, but I can talk more in general about what happens when looking at manuscripts and working out what to do with them.
Firstly. When dealing with literary manuscripts like this, the most important thing to realise (barring a handful of sort of exceptions/complications) is that none of the texts we have are original. We have nothing personally written by Plato or Tacitus, just copies of copies of copies of copies of their works. And this causes... problems.
Understandably when you have such a lengthy process of copying long works by hand errors creep in. Many of these are accidental of course. A scribe (who may not necessarily even read the target language and simply be copying the form) makes some sort of error and that error becomes part of the text, copied again in the next version(s) and the next and so on.
Sometimes the process is a little more active. Say I make a mistake and instead of writing 'tacked' I accidentally write 'lacked.' Then when the next copyist comes years down the line, they look at 'lacked' and notice the error. But they misidentify it and recorrect 'lacked' to 'slaked.' So now we're two degrees of separation away from the original.
Other mistakes can be things like Interpolation, something the original author didn't write being absorbed into the whole. If I leave some notes to myself in the margin of the copy, the next copyist might look at that note and not know whether it was an omission that I'd gone back and corrected in the margin, or just my own scribblings.
Again these can sometimes be malicious. Occasionally things are deliberately altered for various reasons (usually the text saying something you don't like for whatever reason.)
The second thing to understand is that most texts have a number of copies floating around. Imagine a tree. The original text is the trunk and each copy is a branch of the tree above. As you go further and further and more copies are made, more branches appear. Part of the job of figuring out all this out is trying to construct this tree. As an example lets say we have a text with 3 manuscripts, A,B and C. A and C both misspell the same word in the same place while B has the correct spelling. This suggests that A and C are more closely linked to each other than they are to B. Its possible that A is a copy of C (or vice versa) and so has inherited the mistake.
Another possibility is that we can intuit that there's a manuscript we don't have (lets call it D) and that A and C both branch off from that. That's a relatively simple example, but in reality of course its a vastly more complicated job. You're often dealing with far more than a small number of manuscripts and each additional one adds another layer of complexity to this process. Trying to work whether and how manuscripts relate to each other when there are multiple missing branches between them is no easy thing. These are relatively simple examples, but understanding all these relationships can be very helpful in working out where and when mistakes crept in.
Different texts also have different numbers of manuscripts available. The works of the poet Catullus for example are particularly unstable. As far as I recall all known copies branch off a single (now lost) copy in the 14th century Ad. So sometimes there isn't a whole lot to work with
So when a modern classicist comes along years later and makes an edition of a classical text, they have quite the job. They aren't just making a new translation of an existing text, they're also creating a version of the text that they argue is more true to the original. And the rub of this of course is that its very much not an exact science in a lot of cases.
Sometimes of course errors are pretty clear cut. If a word is spelled in a way that has never been seen before then we can say with reasonable certainty that its an error and recorrect it. Although even then its not certain and could easily be something like a slightly different dialect with a different spelling. Many many other cases are not as clear cut.
In particular its very easy to fall into trying to intuit the 'best' version of a text and assuming that that's the correct one. There always exists the possibility that the original author made a genuine mistake and isn't a savant auteur immune to mistakes. For example, if a poet repeats an identical line one after the other, we might assume that they were repeating the line for some sort of dramatic effect, where in reality its an interpolation by someone copying down the line. In that case trying to assume too much intent by the original author tripped us up. Or if Plato is writing a particularly abstract piece of philosophy, do we think there's a mistake there and its genuinely been garbled, or do we simply lack the cultural and linguistic context to fully understand what he's trying to say. Both are possible and are just one of many choices that have to be made. This kind of correction is far more cautiously done nowadays, compared to much earlier scholars who were pretty gung-ho with their corrections...
The final thing to note is that these modern editions are not like copies being made. They have copious notes explaining and justifying their decisions and changes from different manuscripts.
I'll mention very briefly the exceptions I referenced earlier. While most texts don't last 2000 years, Papyri can last that long, if kept in particularly arid conditions. So Egypt in particular, controlled by the Roman and Byzantine empires for several hundred years has heaps of surviving Papyrus that are recovered. Often this means that we get a version (or more realistically a fragment) of a text that is far further down the tree than most copies. As well as this, plenty of original documents are recovered, but those aren't really relevant to this, as they were never copied in the same way. The other exception that comes to mind is something like the Villa of the Papyri in Herculaneum. The town was buried by Vesuvius and an entire library of Papyri was carbonised and essentially burnt into blocks that modern techniques have had some success in reading. Again these are much further down the tree but still not original
So the main thing to emphasise is that framing it as a manuscript being reliable or not slightly misses the point. All manuscripts are treated as suspect to a certain degree, and a lengthy process goes into trying to divine the most accurate version. Of course there is, and never will be a way to know for certain how close we are to the original. But that doesn't mean its not worth doing or that efforts to do so are completely worthless. Its just a matter of doing the best we can. I also want to emphasise again what a difficult thing it is to do. The people who are able to do this often spend years doing so. I wish I had their talents :'(
Reading through what I've written I think this makes sense? (fingers crossed)