There are a number of potential issues in this case. One is whether the combination of drugs causes unnecessary risk of pain and extreme suffering. When the execution isn't botched, the first drug is supposed to render the prisoner unconscious, the second drug paralyzes them, and the third drug causes cardiac arrest. The process should take about 20 minutes.
Except for when it doesn't. The use of this cocktail is barbaric - animals are put down with more humane drug combinations. The potential scenario at issue? The first drug does not fully render the prisoner unconscious, putting them at risk to feel the excruciating pain of cardiac arrest. But the prisoner won't be able to scream or communicate that they're in pain because the second drug has paralyzed them. A number of renowned doctors have testified that this horrifying scenario is a very real possibility with the three-drug cocktail.
The decision in this case could well have nationwide implications: 37 of the 38 death penalty states use the same three-drug cocktails. And as recently as last week, a federal court judge ruled against Tennessee's use of the same cocktail, finding it caused "a substantial risk of unnecessary pain." Today, The Washington Post reported that a scheduled execution in Virginia will likely be put on hold pending the Supreme Court's decision in Baze.