Deadlines are cut off points arbitrarily drawn by committee members. Although they may have some importance or they would not have made the deadline when it was, in the end accepting Armstrong was the right move. If the person's application is good enough for them to be considered an asset even past the deadline, then the astronaut should be accepted.
Yes, it should have. We needed talented and courageous men in space. This is an instance where bureaucratic red tape could have had devastating effects on not only the burgeoning space program but on history in general. A little wiggle room should certainly have been made for the great Neil Armstrong.
Neil Armstrong's application should have been rejected. This is another case of who you know and not what you know. If he did not have a friend in the right places, his application would never have been accepted because it was a week late. Deadlines are in place for a reason and in all fairness, his application should not have been accepted. Other candidates whose applications were late were rejected for that very reason. His should have been as well.
Well obviously deadline's exist for a reason. If he missed the deadline he shouldn't have been allowed as an applicant. The issue is that nobody (other than his friend who put his application into the pile) knew that he missed the deadline. They obviously weren't too concerned about the deadline themselves. If they didn't care that much, it makes sense that they'd let him in still.