How do you know if a beer is oxidized?
That's not the start of a joke - if it was, it'd be a pretty boring one. It's a sincere question. The trouble is that, very often, you'll be told the answer is, "it smells like wet paper or cardboard." One reason you'll hear that is because, sure, sometimes a beer is so oxidized that it actually smells like wet paper or cardboard - old, pulpy, and stale.
Another reason you'll hear it is...because that's what we tell people to say when they think a beer is oxidized. Most beers that are oxidized, though, won't smell like you just dipped your Sunday New York Times into last night's leftover pint of Pilsner. It'll just taste duller than it would have, and that's if you're lucky.
The False Spectrum
For lots of beer diagnosis, we (wrongly) treat signs of an off-flavor as though it's just a question of amplitude or spectrum. If a beer is oxidized, it's going to smell like paper - slightly oxidized, a little paper; much more oxidized, a lot of paper. If a beer is contaminated, it'll taste a little sour; more contaminated, a lot sour.
It's an awfully simplistic approach, and one that's woefully inadequate and probably invalid.
This "false spectrum" disorder that we seem to have is probably a result of our relative palate inadequacies. If we had sterling palates, all of us, and could detect and disentangle each individual sensation and flavor, then maybe we could speak in these terms - but we can't. Don't believe me? Watch a cooking show, and see how professional chefs struggle with identifying something as exotic as "chicken" while blindfolded. Or pour four samples of four IPAs for your friends and see if they can tell you which one is which even after you tell them what you've poured (and it's a virtual impossibility without narrowing the field for them).
So if we're not tasting machines that can parse out all of those flavors - minutely and precisely - then what's the answer?
See the Whole Off-flavor Crime Scene
Don't look for one piece of evidence - look for all of them. Yes - an oxidized beer may well taste like wet cardboard (and if you've ever unpacked beer shipped to a competition, you know that smell perfectly, because it's how about one in ten of the shipping boxes smell because some of the beer has leaked out). But that's not the only way to detect oxidation (and, I'd argue, it isn't even the most common).
Instead, let's think about what oxidation is, and what it does.
Oxidation is effectively a consumption process. Iron oxidizes - it is processed from iron into rust. Gasoline oxidizes - it is converted from fuel to heat and exhaust. Beer oxidizes - and sometimes it converts into a detectable aroma of staling.
But the staling is happening even if it isn't sufficiently intense to be detected by your nose.
Compounds in the beer that would ordinarily produce other flavors, won't, because they've been converted into something else.
The Dog That Didn't Bark
Look for the dog that didn't bark. A beer that has flavors that seem dull, muted, absent, or different-than-expected may well have an oxidation problem, even if you can't smell paper.
A friend says that he added a bunch of late hops, but there's little hop aroma? Could be an oxidation issue.
A homebrew club member says that she made a great Saison but it lacks esters and phenols? Could be an oxidation issue.
Consider secondary factors to try to see if this might be a cause. Ask when the beer was brewed. Ask how it's stored, and for how long. Ask if it's kept at a constant temperature or if it fluctuates. Ask if they flush their kegs with CO2 before racking into them.
Because, often, you're not going to have that positive and patent evidence of oxidation - but that doesn't mean it isn't there.
The Dog That Barked Too Loudly
Sometimes, too, evidence of oxidation will be too pronounced to diagnose it properly.
Once upon a time, about a year into my brewing habit, I played around with bottle conditioning beer directly in growlers. It seemed like something worth exploring, as a sort of "middle ground" between bottling and kegging, and I was often taking growlers places anyway. The concern (initially) was that the threaded caps wouldn't be up to the job, and would simply leak out CO2. But two weeks later - Eureka! - growler-conditioned beer.
But it had a problem: there was an acetaldehyde (green apple/raw grass) flavor that wasn't present in the conventional bottles. It puzzled me, and no one I spoke to had an answer, so I e-mailed a gentleman by the name of John Palmer. He shared my befuddlement, but speculated that what might be happening was an excess of oxidation: apparently, sufficient oxygen post-fermentation can actually cause ethanol to revert to acetaldehyde - bingo.
It's worth noting, though, that the beer never gave the traditional "wet paper" aroma we (supposedly) associate with oxidation. It's not a good idea to get too tunnel-visioned when it comes to presentation of off-flavors - either in small or large presentation.
Simple Isn't Always Precise
I know this might seem to run a bit contrary to my usual philosophy, but in this case "simple" isn't synonymous with "precise" or "minute" or "discrete."
There are times when holistic assessment is better than fine-grain analysis. Stand back and see if you have secondary or atypical or unexpected or should-have-expected signs of oxidation, and if you do, tighten up, particularly on your cold-side beer handling. It's still simple - it's just higher-altitude. Macro. Big-picture, which comprises lots of smaller elements.
And if you suspect oxidation, what then?
Use CO2 liberally at kegging. Cap on foam when bottling, and make sure you're fully seating those caps. Store beer cold, and at a steady temperature to minimize the unavoidable "breathing and sucking" of bottles that are experiencing temperature fluctuation. If you're doing all that, maybe shift to hot-side causes - are you using old ingredients, or splashing the wort excessively? Lots of causes of oxidation out there, and most can be addressed passively.
Failing to do so might be causing subtle (or major) problems in your beer that have nothing to do with wet paper.
Keep it simple.