Are there differences in DNA between humans of today and humans from 2000 years ago?
The larger differences are most likely in epigenetic marks on the DNA. The environment is a lot different today than it was 2000 years ago and those differences are stronger determinants of epigenetic change than sequence change.

2000 years is only about 40 generations and that is not very much to see great differences in DNA sequence or allele frequencies - once founder populations are removed from the analysis.

Height is highly influenced by genetics, but can be masked by environment - notably diet. Diets higher in protein content are more likely to elicit the expression of the "height alleles" but only to a point as too much protein is also unhealthy.

Added in Edit 4 Apr 2012: I should add that my response is written from the perspective of frequency of alleles or epigenetic marks across a population.