Why is my AirTag showing incorrect locations for my pet?

It is important to understand two things about AirTags:

1. An AirTag does NOT know its location. It relies on a nearby iPhone, that is participating in the Apple Find My network, to relay the tag's encryped ID, along with that phone's GPS location to the Apple servers over an active Internet connection. This is where you would see the "tag's" location updates with the Find My app on your iPhone.
2. When an AirTag is outside the Bluetooth range (~30-40) of your iPhone, it relies on that Find My network. If no other iPhone gets within Bluetooth range, there will not be any location updates. In this case, it may be possible that those "locations" were other iPhones that got within range temporarily to relay the data to Apple.

Bottom line? The AirTag makes for a poor tracker for pets. Not only does it only provide sporadic, and often inaccurate, location information, the tag can "beep" periodically which can be very annoying to pets. If your goal is to keep track of your pet, then I suggest you consider getting a tracking device that is based on GPS technology and not Bluetooth. Apple primarily designed them to help you locate a stationary missing object, like misplaced car keys.