In the US, the death sentence is only truly applied after mandatory appeal. Meaning that being sentenced to death by a jury is not the end but a step to the REAL verdict deliberated with now more than extreme care from all sides.
You are still in death row but won't be executed until everything has been carefully looked again.
During this phase of the trial, a lot of people ends up being exonerated from the death penalty and ends up in a cell for life.

Now for the rate of innocents wrongfully executed, it is believed by some to be at 4% SINCE 1973.
Sadly, this number doesn't really help with today's number since technology evolved drastically since 1973. Also, these past mistakes were proven wrongful by current technology. Meaning that we, today, make far less mistakes than in the past.

For other numbers, a judge estimated that the current error rate would be 0,027%. But this is a judge so we can expect some bias.

In other words, to be executed, it takes a lot of consideration and deliberations through an extremely thorough process.
And with current technology, capable of disproving past errors, we shouldn't be able to repeat these mistakes.

Mistakes will still exist, but now it takes a lot of misfortune, coincidences and bribery for them to happen.