Sometimes multi-judgment cases challenge the analytical powers of readers. Especially when there is no headnote, and also when they seem to be of only marginal interest.
Thanks to David Cohen's interesting comments on McDonald v Chicago  USSC No 08-1521 (28 June 2010) I can mention that state and local anti-gun laws might be unconstitutional. A headnote is provided for this case, but it is so complex that only students of US constitutional law would be motivated to study it.
What I do find interesting is Professor Cohen's point that this case is an example of a paradox. It seems (I rely on his analysis) that the reasons for holding the relevant law constitutional were accepted by more judges than those who found reasons to hold it unconstitutional, yet the outcome of the case was that the law was unconstitutional.
The "paradox" of there being an excess of judges supporting some of the reasons for what turns out to be the minority conclusion is illusory because the total judicial support for those reasons consists of dissenting judges who regard them as adequate, and majority judges who do not. The decision in the case is supported by reasons held to be adequate by the majority of judges. If any of the majority judges indicate support for reasons relied on by the minority, those judges are not thereby lending support to the dissenters' conclusion.
Was the relevant law in McDonald unconstitutional? Four justices held yes, because it infringed the due process part of the Fourteenth Amendment, and one justice held yes, because it infringed the privileges and immunities clause of that Amendment. So, five justices held the relevant law unconstitutional. That being the majority, that was the decision.
It is true, but irrelevant, that in some respects these majority justices recognised reasons that would have been insufficient to support their conclusion. Their partial agreement with reasons relied on by minority justices does not add to the tally of dissenting justices.
What matters for the result is how many justices found at least one reason to hold the relevant law unconstitutional. Five. The number of justices who found no reason to hold the law unconstitutional was four. It is a fallacy to say that a justice who finds only one reason to hold the law constitutional should vote constitutional.
The reasons for the decision of the Court are not the same as the reasons for the individual judgments. When asking what the case is authority for, one looks at the reasons for the decision of the Court: McDonald is (again, relying on Professor Cohen's summary) authority for the proposition that the due process requirements of the Fourteenth Amendment render unconstitutional the laws considered in that case.
Professor Cohen's "paradox" is not really a paradox. It is a mundane result of what is sufficient reason for a decision.
Now that you are in the mood for analysing multi-judge cases, have a look at R(Smith) v Secretary of State for Defence  UKSC 29 (helpfully discussed by Alex Bailin QC and also by Aidan O'Neill QC). It deals with the extra-territorial effect of the European Convention on Human Rights, and American readers who see the big picture might compare it to Boumedeine v Bush, noted here 13 June 2008.