- The following list is something I provided previously. Which specific claim would you like me to address first?
The Carbon Dating is suspect.
1. The emotionality in the 10 years of negotiation leading up to the test.
2. Significant protocols determined, but not followed.
3. The size and location of the sample.
4. Potential of repair, contamination and “new” linen.
5. Church (rather than scientists) selects sample.
6. Sample selected at the last moment, after two hours of “ecumenical” debate.
7. Final step in procedure seen by only 2 people, and not videotaped.
8. No test for chemical composition.
9. No archeologist involved.
10. STURP deliberately excluded.
11. Gove eventually excluded.
12. A clear age gradient within the sample.
Here’s a quote from “The Coming of the Quantum Christ” by John Klotz.
[Professor Emanuela] Marinelli related to the Valencia Conference [in 2000] how competent scientists attacked the execution of the process and charged the labs with concealing the data necessary to determine adequately what they had done in their experiments. She cited a fifteen point critique of Philippe Bourcier de Carbon delivered at an international symposium in Rome in 1993: 14 (1) Absence of a formal report of the sampling; (2) Absence of a video archive on the final steps of the samples packaging; (3) In the official reports, contradictions about the cutting and the weight of the samples by people in charge of the sampling (4) Breaches of the protocols initially planned for the operation of dating; (5) Rejection of the usual procedure of double-blind test; (6) Refusal of the interdisciplinary documentation, which is usual in the procedures for radiocarbon dating; (7) Exclusion of acknowledged specialists in the Shroud, particularly American scientists who participated in previous works of STURP; (8) Communication to the laboratories, most unusual, of the dates of the control samples prior to testing; (9) Intercommunication of results among the three laboratories during the job; (10) Disclosure to the media of the first results before the delivering of the findings; (11) Refusal to publish raw results of the measurements (requested also with insistence in its official statement by the Scientific Committee which prepared the Symposium in Paris in 1989); (12) Non-explanation of the unique isolation of the confidence interval of the measures performed by the Oxford laboratory compared to those made by other laboratories; (13) Unacceptable value of 6.4 published in the journal Nature for the chi-squared statistical test on the results of the radiocarbon dosage on the Shroud; (14) Rejection of any cross-debate on the statistical measures performed; (15) Rejection, absolutely uncommon, of the publication of the statistical expertise of this operation, officially entrusted to professor Bray of “G. Colonnetti” Institute of Turin (requested also with insistence in its official statement by the Scientific Committee which prepared the Symposium in Paris in 1989).
Numerous respected scholars do not accept the carbon dating as final. For example, from
http://shroudstory.com/:
Even the famous Atheist Richard Dawkins admits it is controversial.
Christopher Ramsey, the director of the Oxford Radiocarbon Laboratory, thinks more testing is needed. So do many other scientists and archeologists.
Philip Ball, the former physical science editor for Nature when the carbon dating results were published, recently wrote: “It’s fair to say that, despite the seemingly definitive tests in 1988, the status of the Shroud of Turin is murkier than ever.” 
