When did the apostles "see the Son of Man coming in his kingdom?"

"For the Son of Man is to come with his angels in the glory of his Father, and then he will repay everyone for what has been done. Truly I tell you, there are some standing here who will not taste death before they see the Son of Man coming in his kingdom." Matthew 16:27-28

Lets make some observations about the text. 

1. Who was Jesus talking to? "His disciples" (16:24), but Jesus said only "some of you standing here" (16:28), therefore not all of them would see. When Matthew says "disciples" he does not necessarily mean just the twelve apostles, though I think we can assume that the twelve were implied to be there. I think it is safe to assume as well that Jesus was including at least one of the twelve in the group that would see him coming in his kingdom. 
2. What is the context? Jesus is explaining what he demands from his followers and giving them perspective and reasons for why they should follow him. (16:24-26)
3. Who is "the Son of Man?" The Son of Man is Jesus himself (16:13-15)
4. What event is "the Son of Man coming in his kingdom?" It seems to be the second coming of Christ, since it is the same event as verse 27 in which Jesus says that he will come with his angels in the glory of the Father to judge the world. (Could possibly be figurative but would be very difficult to justify that)

The second coming of Christ hasn't happened yet and haven't all the apostles died? Did Jesus prophesy falsely then? 

I think we need to take a little bit of a closer look at the text. Specifically Jesus says that some of them will "see the Son of Man coming in his kingdom." This implies an event similar to when Jesus ascended into heaven (Luke 24:51), specifically when he descends in the second coming (Acts 1:11). 

"Then I saw heaven opened, and there was a white horse! Its rider is called Faithful and True, and in righteousness he judges and makes war. His eyes are like a flame of fire, and on his head are many diadems; and he has a name inscribed that no one knows but himself. he is clothed in a robe dipped in blood, and his name is called The Word of God. And the armies of heaven, wearing linen, white and pure, were following him on white horses. From his mouth comes a sharp sword with which to strike down the nations, and he will rule them with a rod of iron; he will tread the wine press of the fury of the wrath of God. On his robe and on his thigh he has a name inscribed, "King of kings and Lord of lords." Revelation 19:11-16

Who said "I saw" in this passage? John (Revelation 22:8). Well anticlimactically I think that this is the answer to the question. John saw a vision of the second coming of Christ before he died; he wasn't actually present for the second coming.  From what Jesus prophesied we can conclude that other disciples also saw visions of the Son of Man coming in his kingdom. 

Early on the apostles thought that "the kingdom of Israel" was going to be restored in their life time, 

"So when they had come together, they asked him, 'Lord, is this the time when you will restore the kingdom to Israel?' ". Acts 1:6

They probably thought that Jesus' prophesy supported this idea. But they had both the timing and the fundamental details wrong.