In Unity, Jesus isn’t superior to us. We don’t need to give the right answer or win his approval in order to be saved. This is because our salvation isn’t in his hands. He just shows the way.
In Unity, access to Heaven isn’t limited to those who follow Christ (ie Universalism). But it depends on what is meant by “Christ” and “follow”. Christ has two meanings in New Thought: (1) Jesus Christ the Wayshowher, and (2) Christ Consciousness. New Thought Christianity is non-exclusive. Most New Thought practitioners probably see Christ Consciousness in all religions. The language used isn’t important. It doesn’t matter if you call this Wayshower principle Jesus or Buddha or whatever, and there is no reason why there can’t be multiple Wayshowers. In New Thought, to “follow” Christ simply means to live your life according to his example. This doesn’t necessitate believing in the one true dogma or accepting Jesus as the one true savior. It simply means that you follow him and so all that it implies is that you trust his guidance, that you trust he knows the way. Also, New Thought practitioners tend to believe that there are many paths to “Heaven”.
In Unity, Heaven and Hell don’t exist as separate realms. They’re states of mind and they’re part and parcel with how we live our lives, our words and our deeds. We don’t have to wait until we’re dead to be close to God. Sin is our separation or rather perceived separation from God, but there is no Original Sin. Sin like salvation is in the present. Each moment gives us an opportunity to accept or deny God.
In Unity, we co-create reality with God. It is difficult to trace this idea. One of the earliest source would be Gnosticism. There is an idea that began in Gnosticism and was adapted in later Kabbalah. The idea is that we don’t merely passively receive salvation but rather participate in the salvation process.
New Thought types like to quote passages such as Psalm 82:6 and John 10:34. New Thought interprets as literal truth the statement of Jesus that “You are gods.” And in John 14:12, Jesus says “Verily, verily, I say unto you, He that believeth on me, the works that I do shall he do also; and greater works than these shall he do; because I go unto my Father.”
Also, Mesmer had the idea that we have the power to influence our reality. Phineas Quimby is considered the Father of New Thought and he studied Mesmerism.
I’ve read that Unity began within the Evangelical movement. It doesn’t seem all that Evangelical in comparison to some more vocal Evangelists today, but it still has an Evangelical core. I suppose it was Robert Schuller who first popularized New Thought (he is my mom’s favorite minister). I’ve seen many Evangelical tv ministries where New Thought ideas are preached. What is known as prosperity thinking in New Thought and positive thinking in New Age is called by a different name in the Evangelical movement. Its called prosperity gospel or abundance theology. The newest popular proponent of New Thought in Evangelism is Joel Osteen.
The wiki article says…
Universalism is a religion and theology that generally holds all persons and creatures are related to God or the divine and will be reconciled to God. A church that calls itself Universalist may emphasize the universal principles of most religions and accept other religions in an inclusive manner, believing in a universal reconciliation between humanity and the divine. Other religions may have Universalist theology as one of their tenets and principles, including Christianity, Hinduism, and some of the New Age religions. Universalist beliefs exist within many faiths, and many Universalists practice in a variety of traditions, drawing upon the same universal principles.
The most common principle drawn upon is love. (Sai Baba/Baba Speech): “The spirit present in all of the beings is varily seen as that of mind. They are all full of the essential love. Without love, it is all just a pun, without love you can not be happy !”
Truth is also an important principle to be drawn upon. The living truth is more far-reaching than national, cultural, even faith boundaries. 
That generally lines up with my understanding of Unity’s Universalism. The Random House definition says that “the doctrine that emphasizes the universal fatherhood of God and the final salvation of all souls.” Within the Unity church, fatherhood isn’t a term that I remember hearing much in reference to God, but the general idea of God’s universal nature as Creator has a similar meaning. The major difference here is that Unity wouldn’t agree with a view that final salvation is a collective future event. This goes along with heaven and hell not being places that we go to. Ultimately, Unity teaches that everyone is already saved. Sin is an error in perception and that is all. We aren’t really separate from God because everything is eternally in and of God.
There are all kinds of weaknesses some inherent to New Thought theology and some with how New Thought has manifested in contemporary culture. Most importantly is the question of whether New Thought aligns with what psychological research has discovered. Some of the strongest criticism of New Thought in its relationship with New Age comes from the Integral theorists. A book that looks interesting is The Dark Side of the Light Chasers by Debbie Ford. I haven’t read the book, but it seems to be about how some New Agers could learn a thing or two from Jungian shadow work.
In highschool, I was heavily influenced by both Unity and A Course In Miracles (ACIM). This means that the two are pretty mixed in my mind. The ACIM was popular in Unity. Because of this, Unity decided to stop carrying it in their bookstores. They were worried that people would start thinking of Unity theology only in ACIM terms. The ACIM has much more of an intellectual theology than New Thought does in general, and so ACIM adds a bit of meat to the bones. Check out Kenneth Wapnick if you’re interested in the theology pertaining to the ACIM. Basically, the ACIM is most similar to Valentinian Gnosticism.
I’ve studied the ACIM more thoroughly than I have ever studied Unity theology. As I was raised in Unity, I never gave it much thought growing up. And as I haven’t attended a Unity since highschool, I’ve never studied of its theology to any great extent. I’m not an expert on Unity, but its essential philosophy is easy enough to grasp… easier to grasp than the historical comlexities of Catholic theology. The funny thing about Unity is its lack of motivation to push a particular theology beyond a few basic beliefs. I was never taught what the beliefs of Unity were. I never even read the Bible growing up nor do I remember anyone reading Bible stories to me. It didn’t even occur to me to think about any of this.