Landing on the FBI's terror watch list can prevent you from boarding an airplane, but evidently it does not prevent you from buying a gun. From Huffington Post:
There were 963 people from the watch list who were recorded trying to buy guns in the last five years, according to a new Government Accounting Office report. Well over 800 purchases were permitted under the current law. Only 10 percent of all those who tried to purchase guns were actually turned down.
It seems to me that these 800+ people either do not belong on the watch list, in which case they should be able to challenge their inclusion on the list to remove their names and allow them to fly without harassment, or they have rightfully earned a spot on the list and we shouldn't be giving them guns. I look forward to the due process arguments coming from the gun-advocate senators who have been deaf to the due-process concerns of the watch list otherwise.