I would assume that when he spoke about inequality he was talking about injustices about the asking for the death penalty itself when it comes to race, area of the country and financial realities of defendants. Also, some police investigations are way more capable than others. That capability can be because the police kept an open mind when investigating and not trying to convict the suspect they have by ignoring other evidence that does not fit their investigation. In other cases a confession is obtained by the police due to plea bargaining with other suspects who can make their own part smaller and enlarge the part of the other suspect. Then there are jailhouse snitches who get a lower punishment etc. for "testifying" on what a suspect supposedly will have said.
In a perfect world the police would still investigate the case vigorously after that confession to make sure that the right person is indicted and not one of the other co-defendants was the true criminal but sadly I have a sneaky suspicion that this may not happen.
Sometimes the police beat the confession out of a suspect or force him to make a statement even though it is not the truth just because they will then will no longer be interrogated aggressively by the police.
Sometimes the police beat out that confession, have a suspect eyewitness account and then do no further work and just go for the conviction. It is sad but true but not all police forces/offices competently perform their duties.
I may be wrong but I thought his point was more to do with the fact that different States have different requirements for the death penalty.
The following aggravating circumstances constitute capital murder in the state of Arizona:
prior conviction for which a sentence of life imprisonment or death was imposable;
prior serious offense involving the use or threat of violence;
grave risk of death to others;
procurement of murder by payment or promise of payment;
commission of murder for pecuniary gain;
murder committed in an especially heinous, cruel, or depraved manner;
murder committed while in custody;
murder of a victim under 15 years of age or of a victim 70 years of age or older; and
murder of a law enforcement officer.
Whereas Texas' looks like this:
With one exception, the only crime for which the death penalty can be assessed is "capital murder".
Unlike the Model Penal Code (which does not specifically define the crime of capital murder), the Texas Penal Code specifically defines capital murder (and, thus, the possibility of the death penalty as a punishment) as murder which involves one or more of the elements listed below:
Murder of an on-duty public safety officer or firefighter (the defendant must have known that the victim was such)
Intentional murder in the course of committing or attempting to commit a felony offense (such as burglary, robbery, aggravated sexual assault, arson, obstruction or retaliation, or terroristic threat)
Murder for remuneration or for promise of remuneration (both the person who does the actual murder and the person who hired them can be charged with capital murder)
Murder while escaping or attempting to escape a penal institution
Murder while incarcerated with one of the following three qualifiers:
While incarcerated for capital murder, the victim is an employee of the institution or the murder must be done "with the intent to establish, maintain, or participate in a combination or in the profits of a combination",
While incarcerated for either capital murder or murder, or
While serving either a life sentence or a 99-year sentence under specified Penal Code sections not involving capital murder or murder.
Multiple murders (defined as two or more murders during the same "criminal act", which can involve a series of events not taking place at the same time)
Murder of an individual under ten years of age
Murder of a person in retaliation for, or on account of, the service or status of the other person as a judge or justice of any court
The Texas Penal Code also allows for the death penalty to be assessed for "aggravated sexual assault of child committed by someone previously convicted of aggravated sexual assault of child". The statute remains part of the Penal Code; however, the Supreme Court of the United States's decision in Kennedy v. Louisiana which outlawed the death penalty for any crime not involving murder nullifies its effect.
The Texas Penal Code also provides for the crime of "Capital Sabotage", which while being essentially the same as Capital Murder (the statute provides for the death penalty for "sabotage directly resulting in death") is still listed in its own section of the Texas Penal Code.
The Texas Penal Code also allows a person can be convicted of any felony, including capital murder, "as a party" to the offense under its "law of parties", a variant of the common law felony murder rule. "As a party" means that the person did not personally commit the elements of the crime, but is otherwise responsible for the conduct of the actual perpetrator as defined by law; which includes:
soliciting for the act,
encouraging its commission,
aiding the commission of the offense,
participating in a conspiracy to commit any felony where one of the conspirators commits the crime of capital murder
The felony involved does not have to be capital murder; if a person is proven to be a party to a felony offense and a murder is committed, the person can be charged with and convicted of capital murder, and thus eligible for the death penalty.
As in any other state, people who are under 18 at the time of commission of the capital crime  or mentally retarded are precluded from being executed by the Constitution of the United States.
You don't even have to physically commit a murder in Texas to receive CP