I'm reading Noah Feldman's Scorpions at the moment and just got the section about Adamson v. California; from the text:
The important question raised by Adamson's case was whether the Fifth Amendment applied in state court. If it did, Adamson's conviction would be reversed. If not, he would be executed.
The Supreme Court decided against Adamson. The Bill of Rights had been added to the Constitution as a check on the federal government, not the states. The only way one of those rights could be applied in state court would be if it were "fundamental to the concept of ordered liberty"--so basic that no system could be considered just if that right were not recognized. According to the opinion in Adamson's case, written by Justice Stanley Reed, there was nothing fundamental about the right not to have a prosecutor tell the jury it could infer guilt from the defendant's silence.
He goes on to discuss Justice Black's dissent in the case, that the "Constitution... demand that all the guarantees in the Bill of Rights be applied against the states." Though Black's opinion was a dissent, it seems to me that it's the prevailing view today: "...every action by a state government, including every conviction in a state court, would have to be reviewed to see if it complied with the Constitution."
Has constitutional law changed that much in the last seventy years? I guess I'd never been under the impression before that in the past, the Amendments in the Bill of Rights could be selectively applied in state court. It would seem to completely undermine the purpose of something like the Thirteenth Amendment if it can be selectively applied.
The significance of the Bill of Rights (the first ten amendments to the United States Constitution) in relation to state laws and state courts is ... complicated.
Prior to the ratification of the 14th Amendment in 1868, the Bill of Rights was "unincorporated" with respect to the states, meaning that state legislatures and state courts were free to enact and enforce laws that violated those rights. The ten amendments simply didn't apply to them: the Bill of Rights dictated only what the Federal government could, must, or mustn't do.
In the case of Barron v. Baltimore (1833), Chief Justice John Marshall, writing for the Court, struck down a lower court ruling requiring the state of Maryland to compensate Barron, a business owner, for profits he lost as a result of a state-funded public-works projects. Marshall argued that the Fifth Amendment's requirement that the government provide "just compensation" for property taken for "public use" did not apply to the state of Maryland, so no compensation was due to Barron. But Marshall went even further, discussing the historical background of the Constitution's ratification and the intent of the Founding Fathers in appending to it the Bill of Rights. The amendments, he explained, were evidently intended to assuage the fears of those who believed that the Constitution would give too much power to the Federal government at the expense of the states. Marshall:
These amendments demanded security against the apprehended encroachments of the General Government -- not against those of the local governments. In compliance with a sentiment thus generally expressed, to quiet fears thus extensively entertained, amendments were proposed by the required majority in Congress and adopted by the States. These amendments contain no expression indicating an intention to apply them to the State governments. This court cannot so apply them.
The Civil War changed this attitude, as it changed so much else about American law and society. The Supreme Court has used the due-process clause of the 14th Amendment ("nor shall any State deprive any person of life, liberty, or property, without due process of law") to "selectively incorporate" certain protections of the Bill of Rights against state governments. This process has proceeded piecemeal over the last century or so, with different parts of different amendments achieving - or being denied - incorporation at different times. Here's a handy summary of what has and hasn't been incorporated. In the Adamson case (1947), the Court declined to incorporate the Fifth Amendment's protection against self-incrimination, but that precedent was reversed in the case of Malloy v. Hogan (1964).
One final, important point: The idea that the Bill of Rights was "unincorporated" with respect to the states - and the doctrine of "selective incorporation" which has replaced it - is specific to the Bill of Rights (amendments one through ten). Neither doctrine addressed or applied to subsequent amendments to the Constitution, including the 13th Amendment (prohibiting slavery), which you mention.