how can you tell if the installer messed up?

Good points about the ceiling fan—had a similar issue myself once. But rattling isn't always installer error. Sometimes it's just wear and tear or even temperature changes causing expansion and contraction, especially with metal brackets or mounts. Had a skylight frame that rattled every winter morning until the sun warmed it up—drove me nuts until I figured it out.

Still, you're right about checking screws and mounts first. Quick fix if that's the culprit. If everything seems tight and balanced, though, might be worth looking into materials or insulation around the fixture. Could be something simple like a missing washer or gasket. Better to spend a few minutes troubleshooting now than weeks being annoyed later...