I usually argue that a critic has heard more records, and thus has more reference points as in how this record compares to the rest. Agree? And is there anything else that gives value to the opinions of a critic?
In response to the first part, I think it's hard to say. Personally, I like it when reviewers clearly have done their homework about an artist or an album or a style of music - it means to me that they're invested in their topic and that's always a good thing. At the same time, it can be interesting to read someone grapple with an album/artist/music for the first time and be completely ignorant of its background/history. Context is important but ultimately it's the cultural object itself that makes and leaves the impression. So I'm not always bothered if I don't feel like the writer has a massive background on what they're writing about.
What I don't like and don't' respect is a writer fronting like they know what they're talking about when it's clear as day that they don't. You see this in pop music criticism all the time - writers who write on rap music as if they've studied it for 15 years when, in truth, they've only just started listening to it. If you're a newbie - don't front like you're a vet. Take me: I just listened to The White Album for the first time in my life the other week. I'd be a fool to try to talk about that album as if I know the Beatles' inside and out because I don't. And if I tried to do that, anyone who actually knows anything about the Beatles could probably look right through me and call bullshit on that. Personally, I see this happen all the time with people writing on hip-hop - they're not experts, they haven't been life-long fans but they're fronting as if they have been and I find that insulting to the intelligence of readers who can smell bullshit like that instantly. It's ok if you're new so long as you're willing to cop to it but most critics want to act omniscient. I know why - no one likes to feel stupid - but I respect honesty as much as I respect knowledge.
In response to your second question, let me answer this elliptically: I recently had lunch with Ann Powers, former NY Times music critic and arguably one of the most important female rock critics of the last 15 years, along with Greil Marcus, the undisputed godfather of modern rock criticism and the topic came up as to why both of them became music writers. Their response surprised me and I've thought of it often since then. I'm paraphrasing here so apologies to Ann and Greil if I get this wrong but both became critics because there was something about a song or album or artist that got under their skin and they needed to find a way to talk about it. When they began to write about music they weren't do it for the artist. They weren't doing it for the consumer. They weren't doing it for an editor or a magazine or a paycheck. They did it for themselves - to see what they could come up with that would adequately articulate what was in their heads and hearts about music. Ultimately, I think if you are true to that goal, then it doesn't matter if you've heard one album or a thousand. It doesn't even matter if anyone but yourself reads what you have to write - if a writer can accomplish the goal of really getting out what they want to say about music, that's an achievement in and of itself. I think if you read a lot of music criticism - the cases where you know the reader has nailed it for themselves - THOSE are great pieces to read regardless if you agree with the opinion. Right now, I'd offer up Sasha Frere-Jones' piece on Timbaland and the Neptunes that came out in the New York Times. It's just so obvious that Sasha said what he's been dying to say about Timbo and the 'Tunes. Plain as day and that is one of the things that makes the piece so compelling. It's not the only thing - Sasha clearly knows these artists, their body of work, what they mean to pop music in general, but that's called doing your homework. Sasha goes beyond just reporting background - he makes a statement about why these producers matter and it's a compelling, articulate argument. He just nails it cold and you know he does.
I'm not sure if that answers your question exactly but like most things, you know good criticism when you see it. There's no checklist you can run through insure that what you write will be good or valuable. Ultimately, that's for history to decide, not us.