Hello doodlebug,
Thank you for your message. If you have not already done so, I would suggest that you read
this thread about the purpose of this section. Please bear in mind that questions asked in this section will not be discussed or debated - they will simply be answered to explain the Islamic perspective.
Let me first answer the question in the title of this thread. God has designed humanity as a creation that exists in successive generations. As such, He continues to send prophets to mankind to call people back to the way of God whenever they happen to deviate from the message of the previous prophet. This is out of His Mercy for humanity and to give everyone the opportunity to follow the truth. God will not punish someone for their deviation without sending a Messenger to warn them and call them to the truth.
Jesus, according to Islam was a prophet that came after Moses, right? (please correct me if I'm wrong)
Yes. But he was not the first Prophet to come after Mûsa (Moses) - there were
many Prophets sent to the Children of Israel after Moses and before Prophet Jesus pbuh. Yûsha' bin Nûn, Hizqîl, Ilyâs, Al-Yas'a, Shi'ya, Shamwîl, Dawûd, Sulayman, 'Uzayr, Zakariyyah, and Yahya [peace be upon them all] are the names of some of the Prophets who came between Mûsa and 'Îsa.
Well Moses was a loooong time before Jesus, wasn't he?
Yes.
Why did Muhammed have to appear so quickly after Jesus had come?
Depends on which standard you use to call 600 years 'quickly'. Look at the timespan between the two precedeing prophets: Prophet 'Îsa (Jesus) came
during the lifetime of Prophet Yahya (John the Baptist) - surely that was much more 'quickly'!
If Allah is the one who sent Jesus, and Allah is perfect, wouldn't it make sense that He would get it right the first time and not have to resend yet another messenger to clear things up?
Get what right? Every message was already 'right'. The Prophets are sent to guide back the people to the true message after they deviated. Prophet Muhammad pbuh called people back to the same message preached by Noah, Abraham, Moses, and Jesus, pbut.
Regards