Proof against carbon dating
Some were done by finding lakes with atmospherically derived carbon in their annual layers of silt (called varves).
In those particular lakes, the varves can be counted, and the varves can also be carbon dated. The first kind are datings of things that should't be carbon dated.
Old samples contain much less C14, so the measured date of older samples is strongly affected by even small amounts of contamination.
The third kind are dates which were measured before the 1970's.
Then, we have wood for which we know the right answer.
So, carbon dating has been calibrated against the rings of California bristlecone pines, and Irish bog oaks, and the like.
So, anything more than about 50,000 years old probably can't be dated at all.
In short, unless you have evidence to the contrary, you should assume that most of the carbon in a fossil is from contamination, and is not originally part of the fossil. The nuclear tests of the 1950's created a lot of C14.
Also, humans are now burning large amounts of "fossil fuel".
As the name suggests, fossil fuel is old, and no longer contains C14.
Both of these man-made changes are a nuisance to carbon dating.