The resolution essentially says that the US Justice Systems are too irrepairably broken to admit a fair and just death penalty. In its own words:

.. more fundamentally Section 210.6 is simply inadequate to address the endemic flaws of the current system. Section 210.6, which in many respects provided the template for contemporary state capital schemes, represents a failed attempt to rationalize the administration of the death penalty and, for the reasons we discuss in greater detail below, its adoption rested on the false assumption that carefully-worded guidance to capital sentencers would meaningfully limit arbitrariness and discrimination in the administration of the American death penalty.

It lays out six important reasons for such disrepair [sourced from the actual text of the resolution (in PDF)]:

1. Section 210.6 advocates for an individualized determination of a crime (specifically murder, under certain circumstances) to be considered for death penalty as appropriate sentencing. However, several states have statutory identification of which murders should command the death penalty, and furthermore, such statuary discretion leaves the jury with a ‘formula’ to award the death sentence (rather than individualized determination).
2. Furthermore, the wide scope of murders/crimes that are currently eligible to extract the death sentence, under various state laws, is antithetical to the “spirit” and gravity of the punishment. The problem is that no state has successfully confined the death penalty to a narrow band of the most aggravated cases. Death eligibility in prevailing statutes remains breathtakingly broad, as aggravating
   factors or their functional equivalent often cover the spectrum of many if not most murders.
3. There is an almost unforgivable racial bias in the ratio of the number of minorities sentenced to death compared to the total number. Persistent efforts by various groups to address this issue has yielded little fruitful results in terms of a legal remedy to this issue.
4. The cost of administering the death-penalty is extremely high, and combined with the ineptitude of the defendants’ legal representation, the state incurs high costs in putting people to death who, arguably, do not deserve the punishment in the first place. The resolution noted: “Despite the fact that “effective assistance of counsel” is a recognized constitutional right, the scope of the right and the nature of the remedy have precluded the courts from being able to ensure the adequacy of representation in capital cases.”
5. In light of DNA evidence and upcoming forensic technologies, the acceptable risk of having some persons sentenced to death later, and perhaps too late, be shown to not have committed the crime for which they were sentenced. This issues is highlighted in House v. Bell, in which, the petitioner sought federal review with substantial new evidence challenging the accuracy of his murder conviction, including DNA evidence conclusively establishing that semen recovered from the victim’s body actually came from the victim’s husband, as well as evidence of a confession to the murder by the husbandthe Tennessee Supreme Court refused to consider whether new DNA evidence presented during death penalty appeals necessitates a new trial, and declined to answer other questions posed.
6. The politicization of judicial and gubernatorial elections has made death penalty a campaign issue, which leads to populist-style administration of the death penalty. Additionally, the politicization of the issue of capital punishment in the legislative sphere limits the capacity of legislatures to promote and maintain statutory reform. The kind of statutory reform that many regard as the most promising for ameliorating arbitrariness and discrimination in the application of the death penalty is strict narrowing of the category of those eligible for capital crimes.

In light of these observations, the resolution concludes: “these conditions strongly suggest that the Institute recognize that the preconditions for an adequately administered regime of capital punishment do not currently exist and cannot reasonably be expected to be achieved.”