Alright, so we've agreed that reviews should--indeed, they need to--include plenty of subjective material. We've also agreed that "subjective" can mean anything from common-sense to totally off-the-wall (by reading this far into this post, you've agreed to both these things. Surprise!).
Now, what do we do with that knowledge?
Well, the first thing to do is to try to ascertain how idiosyncratic one's "subjective" complaint (or compliment) is. There's also the matter of communicating that to the review reader. Let's use a made-up example to show what I'm talking about: here's a passage from that timeless classic, "Generic AppleDash Fic:"
"First!" Dash cried triumphantly.We have here a pretty not-actually-awful bit of writing, which nevertheless leaves us with plenty to critique. We can break the specific things down into five categories:
"Ah don' know," Applejack wheezed as she settled down on her haunches beside her friend. "Ah think Ah might'a beat ya to the tree."
"No way!" Rainbow Dash cried. "I totally got here first! Tell you what, let's race back to the--!" She cut off with a wince as her side started to knot up. "Er, actually, maybe we can just call this one a draw."
Applejack smirked. There was something about the way Dash wouldn't take "lose" for an answer that stirred something deep inside her. Dash was cocky, sure, but there was a certain je ne sais quoi beneath that which spoke to the seriousness with which she took not just her racing, but everything that mattered to her. And speaking of stirring, the way Dash was stretching her cramp out gave Applejack a very pleasant view...
Rainbow Dash noticed Applejack staring. "Hey, Earth to AJ. What do you think you're looking at?"
Applejack blushed. "N-nothin'," she stuttered.
1) Criticisms which don't need explication
These are mostly things where simply stating what the perceived problem is communicates clearly to the review-reader (whether that's the author or a prospective story-reader) both what the reviewer took issue with, and whether it's something that's likely to bother them. Examples from the excerpt above might include "Applejack's 'I's are always rendered as 'Ah,' which irks me to no end." Even the vaguer "Applejack's accent is over-written" is probably good enough in a reader-centric review (in an author-centric one, you'd definitely want to include examples); while the review reader might envision something more (or less) dramatic than what's actually in the story, they're not likely to be mislead as to what the issue is, or how it's likely to affect their own potential enjoyment.
2) Criticisms that would be relevant to most readers
This is stuff that the majority of fanfic-readers would agree is an issue. For these, it's always a good idea to explain, at least briefly, what the issue is, and why it's a problem for most readers. That second part is important, because "most readers" can not only leave out significant fractions of the story's target audience, but it often is specifically of less importance to that audience. To use an extreme example, if I complained about the fact that this is a shipfic... well, obviously that's not going to be an issue for virtually anyone interested in reading "Generic AppleDash Shipfic."
If I were going to criticize the shipping here, I'd probably say something like, "I had trouble buying into the central romance, because it comes completely out of left field. AJ and Dash are racing one day, and AJ suddenly starts oogling Dash. There's no buildup, no explanation for what's changed or why she's suddenly hot for RD, just an abrupt narrative introduction of a sexual attraction which we see no sign of in the show." By explaining what my issue is (sudden romantic interest) and laying out why it's a problem (inexplicable in its suddenness, feels contrary to character without further setup), I make clear to anyone who has no problem with those things that... well, that the things I'm complaining about aren't issues that will affect their enjoyment, in ways that "The shipping wasn't well-done" simply doesn't cover.
3) Construction issues
These could theoretically go in category 1, but I'm putting them on their own for two reasons. First, a lot of people will need some explanation to understand technical/construction criticism--not because they're stupid or lazy, but because it turns out that most people haven't taken an English class in a while, and might not have the appropriate terminology on the tip of their tongue (if you are one of those people, you would be surprised how easy it is for those who make a practice of criticism to forget this. Or maybe you wouldn't be). Second, certain kinds of unambiguous construction problems simply don't bother certain readers, and that needs to be recognized, too.
For example, the first three paragraphs of this segment all start with "[quote],[character name][speaking(?) verb]ed"--let's assume that was an equally common construct throughout the story. Rather than just say "the writing style was dull and repetitive," I might instead say "the story, though well-edited in terms of spelling, tends always put dialogue and speaking verbs in the same format. When I came across long stretches of characters talking back and forth, the repetition of style made the writing feel dull and list-like."
On a similar note, rather than say "there are a bunch of strange said-isms here," I would... well, I would say that, but I would append, "...by which I mean words that replace 'said' after character dialogue. The common ones are asked, whispered, etc. This story, despite being very dialogue-heavy, almost never uses the word 'said,' which is a problem because 'said' is basically invisible when you're reading; words like 'gasped' and 'exclaimed' are not, and while you might sometimes want to call attention to how a character is speaking, using saidisms for every line of dialogue becomes very distracting as the story wears on." Again, the kind of reader who thinks "Who even notices this stuff?" can (correctly!) write off the criticism as being irrelevant to their enjoyment, the kind of reader who doesn't know off the top of their head what a "said-ism" is isn't left guessing, and a bit of welcome clarity is provided.
4) Criticisms that are entirely personal
When you have an issue that you know is only going to bother you, it's generally best to either not mention it, or to clearly segregate it from the rest of the review, labeled as such. Let's say I'm someone who gets triggered by ponies using the phrase "Earth to ___," because ponies don't live on Earth, hello?
(never mind that they have used that phrase in canon; I know at least one person who despises any reference to the planet Equestria's part of as "Earth")
Now, I'm allowed to feel that way! But I should also recognize that I'm getting worked up over a casual inclusion that simply isn't going to matter to anyone but myself and, at best, a handful of other people. Again, simply ignoring "Earth" for purposes of the review is a perfectly good choice. If I wanted to say something, however, I might amend a parenthetical aside onto a sentence about wording or worldbuilding, something to the effect of, "(and, although I know I'm being stodgy about this, I still don't like seeing ponies say "Earth to ___!" I know it's just me, but dangit, what's wrong with "Equus?")."
If you are not the fanatical sort of over-parenthesizer that I am, you could also split that off into its own short paragraph, or put it in a footnote, or whatever. Just as long as you make it clear that it's a bit of personal commentary peeking through, and not (exactly) part of the review proper.
5) Criticisms that may or may not be entirely personal
So, when you know that something you want to note is either likely to matter to most people, or isn't likely to, you can deal with it accordingly. What about when you aren't sure?
As in life, I find that honestly is the best policy. There's nothing wrong with outright stating "I'm not sure how many other people will be bothered by this..." in your review, and nobody's going to deduct points (you do know we score all reviewers, right?) if you aren't "authoritative" enough. In any case, just look back at some of the good professional reviewers; there are plenty who aren't afraid to say that they aren't sure how certain audiences will react to something.
Let's say that that "Je ne sais quoi" bit is bothering me. The "problem" is, it's in the narration, and although the narration seems to dip into both characters' heads (something I could talk about via number 3 above), it doesn't take on their vocabularies. It's hard to call the use of a French phrase there "wrong," but it's certainly true that I don't like it, and that I don't think it's a good fit for the writing. And truthfully, I really don't know how many potential readers would be bothered by something like that.
So, if I were reviewing this, I'd say, "As far as the narrator's voice was concerned, I found myself wishing that the vocabulary had been more consistent. When the narration is from Applejack's perspective, for example, I'd have liked to see it be a bit more flavored by her word choice, so that it felt more like her thoughts. Well, that or a completely aloof narrator would have sat better with me; while the story as-written is clear enough as far as understanding goes, I sometimes found myself uncertain whether a line or phrase was supposed to represent a character's thoughts, or the narrator's. I don't think Applejack's the type to think the phrase 'Je ne sais quoi," for example, but on that point, the text is ambiguous."
As with number 2, I want to explain what my issue is (narrator vocab) and why it's a problem (doesn't always fit character), but I want to spend a little extra verbiage here unpacking what could be done to address my issue and what, specifically, it looks like, just in case this is the sort of thing that the average reader will treat more like "Earth to ___" than "shipping out of nowhere."
And there you have it! You are now fully equipped to discuss stories without being the guy who says "I hate AppleDash, this is the worst story ever." Hopefully, if you're trying to put your thoughts on a story into words, this will help you put them into words that don't just reflect your opinion, but which let authors and potential readers act effectively on those opinions.