Why did Peter continue on with the whole prophecy after Pentecost?
Because Peter did not know a 2,000-year break would intervene. Still on covenant and kingdom ground, he could not separate verse 29 from verse 30. He quoted the entire prophecy as if its fulfillments would unfold consecutively, unaware of the coming age of grace.
Les explains that Peter was still preaching on covenant and kingdom ground and had no idea there would be a 2,000-year age of grace. Jesus, by contrast, could stop reading Isaiah 61 at the appropriate place because He knew the remainder awaited a future time. Peter, however, could not place a break between verse 29 and verse 30, so he quoted the whole prophecy as though everything would happen one thing right after another. The Old Testament program, as shown in Psalm 2, gave no hint of a 2,000-year interval; its first half was fulfilled at His first coming, while the second half still waits.