Recent developments in 2005 now indicate the sample cut in 1988 for carbon dating was part of a medieval repair accomplished by skilled weavers in the middle ages. See Latest News for more details on this breaking story.

A good primer on the Carbon 14 dating controversy and why many now dismiss it as flawed.
http://www.shroudstory.com/c14.htm

Here is the original report published in Nature in 1989 from the three carbon dating labs that rendered a date range of 1260 to 1390. The tests have come under great scrutiny and subsequent articles reveal the controversy.
http://www.shroud.com/nature.htm

Remi Van Haelst is an expert in C-14 dating and has shown statistically using the data published in Nature that "the measurements made on the linen of the Shroud are NOT homogeneous and that they should be rejected". He also demonstrates that Nature and the British Museum deliberately biased the tests to obscure the evidence that the sample was not representative of the entire linen. This is a very technical paper but much can be gleaned by reading the summary notes.
http://www.shroud.com/vanhels3.htm

Remi Van Haelst contributes two more articles documenting sampling errors and methodology mistakes with the 1988 Carbon 14 dating tests.
http://www.shroud.it/VHAELST1.PDF
http://www.shroud.it/VHAELST3.PDF