Corrected entry: Where do the resistance fighters get their weapons? They have carried Russian AK series, German UMP's, American M4's and M16's and Israeli Galil series just to name a few. While they might have salvaged the M4's and M16's from US military sources, it is highly unlikely they would find foreign assault rifles and ammunition in the Northeastern United States. That area of the US is notorious for its strict gun control laws.
Corrected entry: The show takes place in the Northeast US where there are many nuclear facilities. Without constant supervision and maintenance, these facilities would start to experience catastrophic meltdowns, causing the entire area to become uninhabitable.
Correction: This mistake entry relies on a number of assumptions. We have never been given a complete back story on the history of the world after the invasion. We don't know what we did with the power plants so we can't make the assumption that they were simply abandoned.
Correction: This is not a plot hole or error, if anything, it's a question. First off, show starts 6 months after the alien invasion; plenty of time for various guns to be moved to the Boston area. Second, many of the fighters were ex-military or ex-police, who would have access to weapons, even in an anti-gun region. Third, we're told a lot of the guns come from Alex Vlensa, a paranoid gun collector who had a vast variety of guns. There are several additional reasons and ways they get foreign weaponry.
Bishop73