There shouldn't be a need for an amnesty on such reports if the company reporting culture is correct. As part of a properly managed SMS, pilots should feel "comfortable" enough to report any "near misses" or transgressions without fear of recrimination. It is by studying such reports and reviewing the circumstance by which the situation arose that procedures and policies can be developed/amended to improve the safety of operations.
Pilots should be encouraged to report situations where they felt less than comfortable whilst flying in accordance with whatever company or regulatory procedures were in force at the time.
As DeltaNg has said, I wonder how many of us have had a "moment" whilst flying at any time, particularly when offshore at night. If these "moments" are recorded, I'm sure that a theme would soon emerge which would then help to develop appropriate changes to prevent the "moments" becoming nightmares!