An interesting study was done on light polarization data from a gamma ray burst that purports to put an upper limit on the granularity of space:

http://www.newscientist.com/article/mg21128204.200-distant-light-hints-at-size-of-spacetime-grains.html

I tend to agree with the author of the article, that it seems difficult to assert that space granularity would have to be smaller than the Planck level. But for different reasons. Since our observational limit is about 18 order of magnitude larger than the Planck level, what would be the point of so many orders of magnitude of additional and unnecessary resolution? A clever reality algorithm can create all sorts of interesting data anomalies!