Have any mutations or genetic loci been associated with exceptional longevity in humans?
It looks like you have uncovered the majority of the corpus of molecular genetics related to aging.  There is a follow up analysis just published this year by Sebastiani et al.  Pubmed has a feature that you can look at the publications that reference the paper you are looking at, and there are only reviews.  Nobody else seems to have done another yet.  

You are probably right to feel that the power of the study is not great.  The researchers did try though. The Centenarians have long lived relatives and the controls had both parents die before they were 73.  Although the controls were 68 y.o. and older.  Yes not great.  The controls are very difficult because you don't want people who would die from heart attacks, hypertension and all sorts of things that would color the background.  Its a hard study to do. 

No single gene will convey a phenotype like longevity.  Its basically impossible as the advantages would propogate through the population v quickly.  We could talk about how this trait is post-reproductive and about the grandmother effect, but I'm setting that aside for now.  

The lack of statistical power of the study is also hampered because a mere 800 centenarians probably reflects dozens of different combinations of longevity groups.  (this is another reason all of these people are of specific european ancestry - to keep the number of variations in combinations down).  There are 281 significant mutations they found.   APOE is by far the most significant (fig1) but given the situation, just focusing on that one is not enough.  

For example, even in flies it looks like the sir2-1 gene is not a single mutant anti aging phenotype.  When they cross the mutant strain with wildtype, the sir2.1 mutants live 15% longer.  Its at least one other mutation they had not detected in that caused a 50% longevity bump in the mutants.  Its probable that if there were 5 other important mutations, that the average crossover has one or more of these mutations with it too. 

In order to try to understand how these loci might work together to expand life span, they created clusters of these SNPs (interestingly half of them are in genes which is relatively rare).  these clusters of genes look like they affect the lifespan together.  the paper is open and all the 281 genes are downloadable, each one of them has a known biological property you can look at.  how they fit together is still to be determined, but their clusters might point the way for now.