While I continue to work on the possible socio-economic differences between similar sized precincts that use different voting methods, I can confirm (thanks to a friend who ran the tests using R) that the differences between the machine counted and hand counted vote totals in New Hampshire's primary are real and significant. When regressed against precinct vote total and vote counting method, the percent differences between Obama and Clinton in the 2008 New Hampshire Primary are statistically significant for counting method.
The P value for vote total (a good proxy for precinct size) is 0.88 (not significant), while the value for voting method is 2.4 E-6 (very significant). In other words, there is a 0.0000024% chance that there is no relationship between the Obama-Clinton percent difference in votes and the vote counting method. So yes, the difference is real. Now there remains the question of whether it can be explained by differences between similar sized precincts that use different vote counting methods. I haven't seen anything so far that points in that direction, but I am still looking.