First, let's examine how to monitor your battery life. While numerous third-party utilities exist for this purpose, I'll focus on just one: the iStat Pro Dashboard widget, which gives you at-a-glance info on multiple details concerning your Mac's hardware, including battery "health." The percentage of battery "health" that iStat Pro shows you is a rough indicator of how your Mac's battery's current maximum charge capacity compares with the maximum capacity of a brand-new battery. In other words, if you're seeing 66% health, that means your battery now holds only 2/3 as much charge as it did when it was new.
Busted battery versus brand new battery
If you don't want to deal with iStat Pro or the Dashboard, OS X has two built-in methods for monitoring battery life. First, you can get a snapshot of your battery's condition by holding down Option and clicking the battery icon in your menu bar. Here you'll see any one of a number of conditions. "Normal" is just that -- move along, nothing to see here. "Replace Soon" means there's nothing technically wrong with the battery, but its maximum charge is somewhat diminished. If you see "Replace Now," it still means the battery isn't "broken" as such, but the charge capacity has significantly diminished.
The final condition, and the one I saw which kickstarted my back-and-forth with AppleCare, is "Service [or Check] Battery." This is the one condition which translates to, "Your battery is well and truly broken. It needs to be fixed."
The second built-in OS X battery monitoring method is located in the "Power" tab of the System Profiler application. This will show you the same "condition" stat as Option-clicking the menu bar, and it will also display the charge remaining versus the full charge capacity in milliAmp-hours.
Old battery versus new battery
Technically, the AppleCare Protection Plan doesn't cover "consumable parts, such as batteries [...] unless failure has occurred due to a defect in materials and workmanship," and the same is true of Apple's limited one-year warranty. How can you tell if your battery has a "defect in materials or workmanship?" It's relatively easy, because Apple provides guidelines for battery life.
"For Apple notebooks with removable batteries -- such as previous generation MacBook and MacBook Pro computers -- a properly maintained battery is designed to retain up to 80% of its original capacity at 300 full charge and discharge cycles." Pretty straightforward, but newer Macs' batteries vastly outperform the older ones. The MacBook Air's batteries are supposed to retain 80% charge capacity after 750 cycles, while MacBooks and MacBook Pros with integrated batteries should retain 80% charge after a staggering 1000 charge cycles.
As you can see in the above comparisons between my old/busted battery and the brand-new replacement, it's easy to tell when your battery has fallen far outside this guideline. In my case, starting at around 240 charge cycles, my battery capacity started falling off from about 86% health -- right about where it should have been -- to 77% within a couple of days. I performed a battery calibration to make sure that iStat Pro and OS X's built-in monitoring weren't throwing up erroneous readings, but iStat Pro's reported battery health still hovered below 80%, and Snow Leopard still gave me a "Check Battery" alert in the menu bar.
Monitoring my battery's performance was easy, and figuring out that something was wrong with it was almost as easy. Convincing AppleCare to replace it was the hard part, and if I hadn't come into my conversation with the AppleCare service rep armed with all the information above, I might not have received a replacement at all.
Quoting Apple's own guidelines back to AppleCare -- "up to" 80% charge remaining after 300 cycles -- I then reported the charge status I was actually seeing, which at the time was 77% remaining after 242 cycles with a "Check battery" status. The rep agreed that I probably had a faulty battery, and he got me an appointment at a local service provider. (I live in New Zealand, which has no official Apple Stores -- in the US, I imagine this whole process would be a lot more streamlined.)
The repair depot's first test on the battery showed no problems. Since this didn't match with the data I was getting from iStat Pro and System Profiler, I asked them to repeat the test. Sure enough, the battery failed the second test, and the repair depot reported their results to Apple.
A couple days later, I got a call back from the repair depot saying that AppleCare had denied coverage for the issue. Here is a point that bears emphasis: if you know you're in the right, don't take "no" for an answer. Knowing full well, based on my own info and the depot's tests, that the battery was defective and therefore covered under warranty, I escalated the issue to the next level within AppleCare and got them to authorize an additional round of tests. Once the battery failed those tests, too, AppleCare finally authorized a replacement.
You don't have to be hyper-vigilant about monitoring your Mac's battery -- a quick status glance once a week or so is probably all you need to do. But if you do start seeing problems, document everything and be thoroughly prepared to argue your case. The more information you have to back up your claim of a faulty battery, the more likely you are to get it serviced or replaced at no additional cost to you.