If you wish to be absolutely correct, you need to take into account the relationship between the thanker and the person being thanked.
So, the problem some of us see with "no problem" is that it is used sometimes by people for whom the task they have done was never supposed to be a problem in the first place, such as the barman who brings you the drink you have ordered.
If you read the wonderful works of PG Wodehouse, you will find that the servant Jeeves's response to being thanked is along the lines "Not at all" or "I endeavour to give satisfaction". Jeeves would never have uttered the words "no problem".
Now, if you were to ask some person whom you regard as very important and in some sense your superior to do something, and they do it, their response to your thanks, could not possibly be "I endeavour to give satisfaction" but could be "it was no trouble" - words that are almost the same as "no problem".