When I read things like this my reaction is, “Well what would constitute a serious rebuttal?” Many young earthist challenges to radiometric dating can be refuted with nothing more than an explanation of the basic rules and principles by which measurement works.
Take for example the claim about carbon-14 in fossils. As @Paraleptopecten has rightly pointed out, we would expect to see trace amounts of carbon-14 in ancient samples because of contamination from modern carbon-14. This is simply one of the most basic, fundamental rules of measurement that applies to every context: you must take into account all possible sources of error, and contamination is one such source of error. Yet young earthists dismiss contamination as some sort of “rescuing device.” By dismissing it as a “rescuing device,” they are demanding that the basic rules and principles of accurate and honest measurement do not apply to them.
Sorry, but no. Accelerated nuclear decay is science fiction. Accelerated nuclear decay on the scale required for a young earth would require the fundamental constants of physics to have changed, and if that had happened then everything would have changed in ways that would have destroyed the Earth.
In any case, it was the young earthists themselves who admitted that the amount of accelerated nuclear decay they needed would have raised the Earth’s temperature to 22,400°C – four times hotter than the surface of the sun and hot enough to vaporise the entire planet. Don’t believe me? Here’s a link to the page in the RATE report itself where they did the calculations.