In court this week, Judge Keller lashed out at the condemned man's lawyers, blaming them for the controversy. She argued that Mr. Richard could still have filed his appeal by seeking out another judge, but that misses the point. She did not follow appropriate procedures. And clearly, under any interpretation of the rules, given that a life lay in the balance, the clerk's office should have stayed open.

It wasn't as if he would've been released into the general population or avoid execution in the long run if the stay had been granted.

 His guilt was undisputed, it seems.  How about some outrage against rapist/murderers?

That's the Straw man argument, again from the Wikipedia:

The straw man fallacy occurs in the following pattern:

1. Person A has position X.

2. Person B disregards certain key points of X and instead presents position Y.
   

Thus, Y is a resulting distorted version of X and can be set up in several ways, including:

   1. Presenting a misrepresentation of the opponent's position and then refuting it, thus giving the appearance that the opponent's actual position has been refuted.[1]
   2. Quoting an opponent's words out of context -- i.e. choosing quotations which are intentionally misrepresentative of the opponent's actual intentions (see contextomy and quote mining).[2]
   3. Presenting someone who defends a position poorly as the defender, then refuting that person's arguments - thus giving the appearance that every upholder of that position (and thus the position itself) has been defeated.[1]
   4. Inventing a fictitious persona with actions or beliefs which are then criticized, implying that the person represents a group of whom the speaker is critical.
   5. Oversimplifying an opponent's argument, then attacking this oversimplified version.

3. Person B attacks position Y, concluding that X is false/incorrect/flawed.
This sort of "reasoning" is fallacious, because attacking a distorted version of a position fails to constitute an attack on the actual position.

Mandatory Link

You could also familiarize yourself with the concept of Due process:

Due process (more fully due process of law) is the principle that the government must respect all of the legal rights that are owed to a person according to the law of the land. As developed through a large body of case law in the United States, this principle gives individuals a varying ability to enforce their rights against alleged violations by governments and their agents (that is, state actors), but normally not against other private citizens.

Due process has also been frequently interpreted as placing limitations on laws and legal proceedings, in order for judges instead of legislators to define and guarantee fundamental fairness, justice, and liberty. This interpretation has often proven controversial, and is analogous to the concepts of natural justice, and procedural justice used in various other jurisdictions.