Why is it important and necessary for other scientists to review the ideas and processes that relate to, and emerge from, new scientific theories?
Peer review is absolutely essential to the process of scientific research. Without peer review, flawed experiments could be conducted and incorrect assumptions taken from data that are collected. The process of peer review ensures that this will not happen.
As far as new scientific theories go, again, it is important for other scientists to review the possible ramifications of these theories. Scientists who come up with theories become attached to them and do not wish to see them disproven or criticized. The careers of these scientists can get to be wrapped up in their theories.
Therefore, it is necessary for other scientists to have a hand in the process. Otherwise, the scientists who are most interested in a given theory will be the only ones to test it.
Great points in the reply above, and here are a few other ideas:
1) As with a medical or economic issue, it's always better to have more than one set of eyes on the problem or idea. Fresh perspectives, different ways of thinking and a scientifically collaborative approach almost always lead to better scientific advances.
2) Science is a competitive field, but also an immensely rewarding one for a society in any number of ways. Sharing this technology through peer review can address or solve many of the world's most pressing problems as scientific discoveries by people in other nations often accelerate the scientific discoveries here at home.