As to the OP question, the case of Bill Wegerle comes to mind. He was the main (and only for a long time) suspect in the murder of his wife, and failed two LDTs, and was later exonerated by the discovery that his wife was actually a victim of the BTK serial killer.
http://www.cbsnews.com/stories/2005/09/29/48hours/main890980.shtml
ETA: Granted, this was in the 1980s, so one would hope the technology is better now, but, still, this case does give me a bit of pause in assigning too much value to LDTs. MOO.
ETA2: Searching for theories/explanations of why Wergerle failed his tests, I found some things (no worth linking - just forums and blogs, mostly) that suggested he was so distraught the findings were off, and/or being told repeatedly that he killed her and that he failed the first test screwed up the findings. I have also seen it suggested that being re-tested rises the anxiety enough to mess with results. All of this should be stuff an experienced LDT tech could adjust for, I should think, but one never knows. I couldn't find an official explanation for his failure, sadly.