What solutions are available for increasing accuracy of the tests? From the source linked above: Carbon-14 is considered to be a highly reliable dating technique.
It's accuracy has been verified by using C-14 to date artifacts whose age is known historically.
The particular example you bring up is one of the most famous such cases.
The claims are really quite spectacular, when taken at face value, and therefore should be examined thoroughly.
Contamination of this kind amounting to 1 percent of the carbon in a sample 25,000 years old would make it appear to be about 1,500 years younger than its actual age.
Let's look at their research methodology in detail (indicated by bullet points): Let's take a little pause to consider the general issue of misrepresenting your own research. did this, since there would have been a slim chance (at best) of the museum curator providing them with any dinosaur bone fragments if he or she had known what the true intent of the supposed chemists was.
In particular, it is implausible that it would have been considered worthwhile to try to use radiocarbon dating methods on these bones, since the rocks that they were taken from were determined to be 99 million years old, as shown in this paper by Kowallis et al.
That included protecting the samples, avoiding cracked areas in the bones, and meticulous pre-cleaning of the samples with chemicals to remove possible contaminants.
Knowing that small concentrations of collagen can attract contamination, they compared precision Accelerator Mass Spectrometry (AMS) tests of collagen and bioapatite (hard carbonate bone mineral) with conventional counting methods of large bone fragments from the same dinosaurs.