We find that [the Jewish people] that [Moshe] was sent to, they were witnesses to his prophecy that it was truth and[, thus, Moshe] did not need to perform another sign for them. For [the Jewish people and Moshe] were witnesses [for his prophecy] similar to two witnesses that see an occurrence together, that both of them are witnesses that the other is speaking the truth and neither of them have to bring proof to each other. Therefore, with regards to Moshe our teacher, all of the Jewish people were witnesses for him after the events of Mt. Sinai and he did not need to perform a sign for them.
[Moshe pursued this course] until G-D made it known [by telling Moshe,] that these signs will only last until the [Jewish people] left Egypt. [However,] after [the Jewish people] will leave and they will stand at this mountain (Mt. Sinai) I (G-D) will remove the suspicion that they suspected after you (Moshe) for I will give you a sign here that it will be known that I sent you, in truth, from the beginning and there will not remain in their hearts any suspicion. This is what the verse [means] when it says (3:12), "This will be for you a sign that I sent you, when you take out the [Jewish] nation from Egypt you will worship G-D on this mountain."
[The only sign that removes all doubts is that the Jewish people saw G-D speak to Moshe with their own eyes, therefore,] you will find the statement that every prophet that arose (or will arise) after Moshe, our teacher, we do not believe in him (or her) solely because of the sign [he or she performs. The reason for this is] because it would be said that if he (or she) performs a sign then we will listen to him (or her) for everything that he (or she) says. However, [the reason we believe this prophet is] because of the commandment that Moshe commanded in the Torah and said (Devarim 18:15), If a sign is given, "to him you shall listen."
[This can be] compared to the commandment that we make a judgement by the word of two witnesses, even though we do not know if their testimony is true or false. Similarly, it is a commandment to listen to this prophet [that has a sign] even though we do not know if it is a true sign or magic and trickery."
The Rambam here is trying to clarify his position as to how valid prophecy is and how it can be utilized. In this halacha, the Rambam is setting up the reason as to why no prophet could ever come to nullify or permanently alter the prophecy of Moshe. His point, although subtle, is that the only prophecy that can be determined to be true by others is the prophecy of Moshe. All other prophets can be lying. This is why all future prophets depend upon Moshe's prophecy and can not contradict his prophecy. This is how the Rambam can immediately brush off any claims of the Muslims or Christians.
I find the Rambam's point of view refreshing for several reasons. Mainly, the Rambam does not believe in mysticism and this idea shines through in this chapter of his Mishna Torah. The idea that one should be suspicious of anything that can not be seen with your own eyes is lacking in most circles. Only in the scientific community, and even then it is not constant, are people only swayed by empirical and reproducible evidence. An argument from authority without any tangible evidence is, according to the Rambam, inherently flawed. The sole reason that we believe Judaism is the correct religion is, simply put, because of the witnessed events at Mount Sinai. Without that single event, according to the Rambam, we would not be obligated to follow Judaism or even believe in G-D.
This point can not be over stated or overemphasized. People who claim to have prophecy or special powers and do not even produce a sign are certainly to be ignored. For, even if they had a sign we can not be sure they are telling the truth. With this as a foundation for Judaism, I think, people would stop making arguments from authority and be more open to intelligent discussions.