"In Florida one in three death row prisoners are subsequently proven innocent. "

The following quoted proportion of judicial failure seemed unlikely, even for Florida:
In the US one in ten death row prisoners are subsequently exonerated.
That's not let off the punishment and put in prison instead, or found not guilty on a technicality;
that's proven innocent.
In Florida it's one in three.

So I decided to determine a more realistic estimate of that proportion.

In the modern era of executions since 1976, following Gregg vs Georgia supreme court decision: http://en.wikipedia.org/wiki/Gregg_v._Georgia there has been 926 death sentences handed down (actually between 1977 and 2008) in Florida.

Of that total of 926

80 convict executed - http://en.wikipedia.org/wiki/Capital_punishment_in_Florida#List_of_individuals_executed_since_1979
6 executions were governor commuted - http://en.wikipedia.org/wiki/Capital_punishment_in_Florida#Clemency
404 convicts are currently on death row - http://www.dc.state.fl.us/activeinmates/deathrowroster.asp
24 death row convicts were subsequently exonerated (as of December 2012 - http://www.deathpenaltyinfo.org/innocence-and-death-penalty#inn-st)

There remain another 412 convicts either who's sentence was reduced by appeal or otherwise died while in custody, or escaped etc.

Assuming that the only category of prisoner who can be truly regarded as having been "proven innocent" are those that were exonerated, then the final proportion is around 2.59%     (24/926)

Some other interesting titbits...

"Alabama, Indiana, and Florida are the only states with laws that allow a judge to overrule a jury's recommendation of life in prison and sentence a convicted murderer to die.

Alabama judges have done it twice.

Indiana judges have done it twice.

Florida judges have done it 70 times."

Miami News, Nov. 19, 1982, at IA, col. 3."

"Because of the lengthy appeals process, more Florida death-row inmates have died in prison (30) since 2000 than were executed (25.) And because of mistakes made in prosecution, more Florida death-row inmates have been exonerated (24) than in any other state."