I googled "Alar Controversy" after Tam noted Meryl Streep's attempt at playing a biochemist testifying before congress...
So I do what anyone would do, I went to pubmed and read as much research as I could this evening.
First, multiple studies have been done with multiple results. Bacteria experiments came back negative for "genotoxic" activity. Rat and mice experiments were much more common, and they all followed roughly the same approach, overdose a population of rodents with Alar and then perform autopsies to look for cancer. What was significant was the amount of time involved in the various rodent experiments.
Anything less than a year came back negative for carcinogenic activity. A study lasting two years found an increase in uterian cancer in female rats.
Now what does this mean? It means rats overdosed on Alar throughout the vast majority of their lives had a slight increase in the rates of cancers of the female reproductive system.
There was an interesting study that showed an increase in rat liver DNA methylation dose dependent with Alar, but I didn't get a good feel for their methodology. Since the other rat studies found no statistically significant increase in liver cancers I question the significance of the correlation.
So, the real question is this, was Alar a threat to children (and supposedly apple eating adults as well)? No, it was not.