The main symptom is that they don’t hold a charge long.
One complication is that people keep adding more and more apps that have more features involving background or periodic activity. These add drain to the battery and may make it appear that the battery is going bad.
One way to differentiate this is how well the phone holds a charge when powered down. When new, charge the phone completely. Power it down. Wait a fixed time like a day. Verify that it is at or near 100%. Once or twice a year repeat. When the value starts to drop noticeably below 100% on one of these tests, you know it is going south. To do this right, you really need to leave it powered off for more like a week to test things. But for some reason a few people don’t like leaving their phone off that long. 
So another way to differentiate is to back up your phone, do a factory reset, and install only the most basic features you need. Use it for a while and see if that helps holding charge. Then you can restore your phone from the backup. Maybe cull as many apps as possible while you’re at it.
(My doctor was complaining at how slow their phone was getting. Was considering getting a new one. All while flipping thru page after page after page of apps on the phone looking for the one they wanted to show me. Um, the phone isn’t slower. There’s way too many apps on it.)
Note that not all cell phones are in a sealed case. So swelling can be checked for those. But by then the short charge holding time is likely apparent.