Matthew 8 really ought to begin in the last verse of chapter 7, which reads:
When Jesus had finished saying these things, the crowds were amazed at his teaching, because he taught as one who had authority...
The chaotic events of chapter 8, which seem to have all taken place in one crazy day, go on to demonstrate Jesus' authority. But not all of those who were there and witnessed these miracles recognized the full measure of authority Jesus had.
Those who completely missed Jesus' authority:
The law teacher and another disciple in v19-21 who seem somewhat interested in following Jesus, but let feeble excuses get in the way of actually submitting to His authority.
The disciples in the boat, who had witnessed Jesus miraculously exercise His authority multiple times earlier in the day, but somehow failed to recognize that Jesus' authority was over all things, even the wind and waves.
Those who recognized some of Jesus' authority:
It doesn't take long for word to spread that this Rabbi who taught authoritatively also could demonstrate it by healing all sorts of ailments. Unfortunately, most of the crowd who clamors around Jesus at this point will never come to realize the full extent of Jesus' authority. They're just interested in having their immediate felt needs taken care of, and miss out on Jesus' authority to solve a much bigger problem in their lives: to take away their sins.
Those who fully recognize Jesus' authority:
The Roman centurion, who not only recognizes Jesus' authority, but also respects it (v9).
The disciples, who after witnessing Jesus calm the storm with one word, are stunned by who and what Jesus is (v27).
The legion of demons possessing the violent men who meet Jesus and the disciples when their boat lands. Upon recognizing Jesus is the "Son of God (v29)," these demons who previously would let "no one pass that way (v28)," don't even put up a fight and beg Jesus to send them into the herd of pigs.