This question has been answered numerous times in the past.
The no-fly list is compiled by government officials in an extra-judicial process. It has included, at one time or another, Ted Kennedy and Stephen Hayes. There are estimates of erroneously placed persons ranging between 40% and 80%, and there is no specific and codified means to remove oneself from the list (I'm sure Kennedy had no problem).
If this list is flawed so must be the terrorist watch list.
If you've never been caught up in the Federal meat-grinder, it all looks so rationale.
This is why due process is one of our fundamental rights because governments will abuse their power.
I've no problem with putting a gun purchase on hold until the Feds make their case why someone on the list is a real threat, but they have to make their case to a judge and quickly. Put a time limit on it. If in 30 days they haven't produced their evidence, the person is presumed to not be a threat.
You surely want to preserve the rights of Muslim-Americans when it comes to this list, but you couldn't care less if the person wants to buy a gun...a right guaranteed by our constitution.