Carbon-14 has a half life of ~5730 years. This is why carbon dating is only used in circumstances where the estimated age is less than 20000 years as I had mentioned previously. The older the item is, the less accurate the measurement becomes but still reasonable up to 20000 years. Long before you get to 1m years there is no carbon-14 left to measure so you cannot get a million year mismatch.

You also shouldn't be dating animals because we consume carbon from our environment in different quantities depending on what we eat so measuring teeth in this fashion will not get an accurate result. Another example is mussels that were carbon dated to be thousands of years old because what they ate had very little carbon in them. Carbon dating is simply not useful for dating animals.

For older things other forms of dating are used such as uranium-lead dating but this is not required for anything built in the time of civilisation (last ~12000 years).

We have lost knowledge due to dark ages. For example we only recently discovered why Roman marine concrete is so strong and durable. I believe in the ingenuity of our forebears.