What did the Jews in Acts 4 have to recognize about Jesus?
They had to recognize that Jesus was the Christ, and only Jesus. Peter declares there is no other name under heaven given among men whereby we must be saved. For those Jewish hearers, salvation was not in Buddha, Muhammad, or any other; only Jesus saves.
Les explains that in Acts 4 Peter is dealing with the Jewish covenant people. For the Jew at that particular time, they had to recognize that Jesus was the Christ, and only Jesus. Peter says there is no other name under heaven given among men whereby we must be saved, and Les emphasizes that this still spills over into our Gospel. The verse is narrow; it brings it right down that there is only one way. Les contrasts this with sincere people today who follow a cult leader, a Buddha, a Muhammad, or whatever. He also notes that many present-day Jews, especially Orthodox, refuse to admit that Jews ever followed Christ, but thousands did early on, and archaeology is proving it. The vast majority rejected Him, and God went to the Gentile, but at this point He is still dealing with the covenant people.