The discovery that all five radiocarbon dates were in the 14th century was a setback for those who believe in its direct association with Jesus; and some have argued that the dates were affected by a fire which added carbon monoxide to the fabric. John Jackson, director of the Turin Shroud Center of Colorado and the University of Oxford Radiocarbon Accelerator Unit conducted additional work in an attempt to identify if carbon monoxide might have been a factor in the dates
Kris provides a link describing what they did here:
The hypothesis put forward in the film is that the linen of the Shroud might have been contaminated by carbon monoxide. Unlike most contaminants, carbon monoxide is naturally enriched in radiocarbon when found in the environment and would therefore in principle be able to alter the radiocarbon age significantly. A relatively small amount of carbon monoxide (roughly 2% of the carbon in the linen) could alter the age of the sample by a thousand years. This is the only contamination hypothesis which could affect the radiocarbon age of the Shroud enough to allow it to be 2000 years old.
They found nothing. Seems like kind of a waste of time since they also note that No contamination like this has been detected before, even on very old samples (up to the 50,000 year limit of radiocarbon) which would be much more severely affected.
But it's a film so it will no doubt be mercilessly hyped and the show will consist of 95% background on the "controversy" with a little bit at the end saying they found nothing BUT IT'S STILL POSSIBLE THAT IT'S THE REAL THING.