Capital punishment has been in the news in the USA recently due to the Davis case and Texas Governor Rick Perry's bid for the US Presidency. In 2004 Perry denied an appeal by Cameron Todd Willingham who was then executed despite scientific evidence that the conviction was flawed. It's then alleged that Perry obstructed a subsequent investigation into the case. The New Yorker published an excellent article on the case. Although long it is well worth the read.
If you don't have time to read the New Yorker's piece then try reading this summary at the LA Times or this Salon interview with a co-director of a documentary on the case. To quote from the LA Times article:
Perry, who may soon announce his presidential bid, oversaw the 2004 execution of Willingham, a father of three convicted for the apparent arson murder of his young daughters. Problem was, the evidence used to prove Willingham set the fire that killed his children was based on shoddy science and obsolete investigation techniques, facts that were brought to Perry's attention before Willingham's death. Declaring his innocence to the end, Willingham was executed 12 years after his children's deaths.Edit 29/9: Time have an interesting article on the unreliability of witness testimony.
Edit 11/3/2015: An article claiming a key witness in the Willingham case was pressured to lie in return for a reduced sentence.