This hardly has anything to do with atheists putting on lipstick but ok, just one:
Ice core dating has always been questionable but the discovery of lost squadron in Greenland showed that the annual ice buildup could be measured in meters rather than inches. Of course the rescuers of the planes were not prepared to dig 250' to find planes that had landed only 50 years earlier. The miscalculation was based on the incorrect assumption that the layers in the ice were annual. Thus the ice core dating was based on a false premise.
Let me anticipate your response:
You will deny that the dating method has been discredited because it was not discredited by the right people. In order for any tenet of evolution to be discredited, it must be done so by evolutionists who have an interest in keeping their jobs.
I grant you that you should not change your mind unless you have adequate reason to change it, but protection of the theory is not an adequate reason to reject all opposing data out of hand.
I'm disappointed that you'd use such a lame example! The Lost Squadron made their emergency landing on the coast of Greenland, where the snowfall is much greater than in the interior of Greenland where all the ice cores are taken.
See here for a good overview and recent news on the Lost Squadron.