First, the New Testament teaches that Jesus knows everything:
Jesus said a third time, “Simon, son of John, do you love me?” Peter was distressed that Jesus asked him a third time, “Do you love me?” and said, “Lord, you know everything. You know that I love you.” (John 21:17)
Second, I read somewhere that Jesus' supposed ignorance of the Day and Hour is identical with His not "knowing" the sinners on the Day of Judgment:
Later, the other virgins came too, saying, ‘Lord, lord! Let us in!’ But he replied, ‘I tell you the truth, I do not know you!’ (Matthew 25:11-12)
Third, most scholars argue that Jesus said He did not know the Day and Hour because the Father did not choose to reveal this knowledge through the Son in human flesh. (This theory has already been brought up by some posters here).
Fourth, Jesus once likens His second coming to a wedding banquet prepared by the King for the Son (Matthew 22:1-2). Thus, it is natural that only the Father know the date of the wedding as he is the one organizing the wedding.
Finally, Jesus is almighty, but once He denies that He has the right to determine who will sit at His right and left:
He told them, “You will drink my cup, but to sit at my right and at my left is not mine to give. Rather, it is for those for whom it has been prepared by my Father.” (Matthew 20:23)
This is a simiar case to the one concerning Jesus' knowledge of the Last Day. In both cases Jesus denies ability and refers to the Father as the sole wielder of authority. Why does Jesus say this? In both instances Jesus' denial shows humility and implies that different requests of men (to know the Day and sit at Jesus' right and left) cause Him to ignore certain things. However, the important thing is that in both cases the central person is Jesus rather than the Father since Jesus is the one to come on the Day of Judgment as the Lord of the House and Jesus is the one at whose left and right the disciples want to sit. It is highly likely that Jesus denied these abilities because He did not want to glorify Himself, but wanted only the Father to glorify Him.