In other words, was there a defect in the revelation in Jesus (whom I understand is embraced as a prophet by Muslims) that was corrected or a truth that was brought forward that was missing from Jesus?
There are a number of issues in this question but I believe at heart it would be useful to answer it in order to clarify a number of misconceptions about Islam that are used by some to characterize Islam in a misleading or disparaging way.
The way the question is posed excludes the true answer to the actual issue, which I would say is essentially "Why was Prophet Mohammad sent after Jesus, since I understand Jesus is considered a prophet of Islam?" By narrowing it down to "was there a defect in the message of Jesus?" or "what was missing or in error in Jesus' message or prophethood to justify sending another messenger?" you request an answer that presumes God made a mistake in sending first one prophet and then another. That presumption is false because God is by definition all-powerful and all-capable and does not make mistakes. Atheists reject the existence of God, perhaps for being defined by that very quality of omnipotence, but allow for the definition of a God as such.
God already foretold the sending of Prophet Mohammad in the Gospel, the Torah, and other divine revelations (this fact not admitted by Jews or Christians who currently have altered versions of the originals), so the sending of these prophets over time is part of God's plan and design and purpose. One discernible purpose is the course of human development and population increase over time created changes in human societies that needed to be addressed by new revelations and new prophets. Life in the time of Prophet Ibrahim (Abraham) was significantly different and people faced different challenges then than in later epochs, and so on. Another purpose is to correct the misunderstandings and lies that people have incorporated into the religion over the years after each prophet, a fact the Omniscient would know.
In the case of Jesus, he is a prophet of Islam, and in no way God. He never said for his followers to worship him or his mother. The Quran will question Jesus on this point on Judgment Day. (This will be a sign on that day for those who worshipped Jesus in this life.) God does not "incorporate", taking on the physical form of anything, or divide into "manifestations" or parts. And when I say "prophet of Islam," it's crucial to point out that Islam is not the name of a new religion as in "now we shall establish a new correct religion and call it Islam", which is the impression many seem to have including quite a few Muslims. Rather "Islam" is a word that describes the essence of faith in God, "surrender" to God as real and beneficial and entirely unique sole Creator and Sustainer of all creation, of the cosmos. Prophet Mohammad is the "seal" of the line of prophets, the last one, but all genuine prophets (and there were prophets in other parts of the world, such as China and India, not mentioned in the Quran, except to say there were "others not mentioned") teach this same religion, with some differences in approach according to the cultures and societies to which the messengers were sent.
And you mentioned Jesus' "sacrifice" in your question. What sacrifice do you refer to? The sacrifice that has now become a part of Christian dogma in which he allegedly is killed on a cross, a slow torturous death, to "save" people from their sins? This is one of the adulterations to the original message of Jesus which the Quran came to correct (among other things, such as the false claim that Jesus came to ask people to worship him as a new god who is part of the old God except more merciful — God forbid that God's mercy should be thought of as deficient while God is All-Merciful). First it blurs the line of definition between Creator and creation, the distinction for which was sent the first commandment. Second, responsibility for one's actions is a prime element of God's religion, and the idea of salvation-by-proxy subverts that. Third, there's no "original sin" in the Christian sense in Islam. No need for that kind of sacrifice. No scapegoating of prophets. How could that be just or fair? God is Just and does not ask us to have faith in absurdities.
Jesus indeed did perform his task as a prophet in the best way and was accepted and honored by God. Nothing was wrong or deficient. It is human interference that brought about over time the dogma that is associated with most Christian doctrines: the supposed trinity or 3-in-1. And 3 will never be 1, so this is inappropriate for a religion of the All-Knowing.
And unlike the Gospel and the Torah, the Quran cannot be tampered with because it is protected by God. One would hope you or others would be curious to know what an unadulterated divine revelation is like. I suppose one could call this protection an "improvement." But in this case, Jesus had miracles as did Moses and many other prophets. Prophet Mohammad's only miracle is the Quran. Appropriate for modern times, the very times for which it was sent.