How could they prove otherwise?
"Palpatine did not appear over night. He was obviously a Senator long enough to get himself rooted in the Senate to get voted into high office. Thus, he was not but a few miles from the Jedi temple. Yet the Jedi could not concern themselves with detecting a Sith Lord just down the street?"
You presume they knew he was the Sith Master that whole time. Again, even if they did, who would believe them? To the rest of the Republic, he was their savior. What, exactly, did Palps do in front of the Jedi that would make them believe he was the Sith Master, to justify their actions against him?
"When you believe your the best, you don't concern yourself with what your competition may be doing. See: Yankees v Red Sox. That's called arrogance."
They were very concerned - they simply didn't know where the root of the problem was. Palps was always two steps ahead, and who, in their right mind, would seriously expect Palpatine to be the Sith Master? He didn't even show any Force use, and couldn't be sensed. What you know to be going on in the films, is quite different from what the Jedi know in the films.
"I have always been confused about this part.....but doesn't a Jedi order the creation of the Army?
Apparently, according to "Labyrinth of Evil", Sifo Dyas ordered the army because he was worried about something happening to the Republic (I've not read the book, so I don't know the specifics.) Not only was his plan designed to protect the Republic (i.e. a good thing), but the rest of the Jedi didn't even know about it (i.e. naivety.) In fact, had Dooku and Sidious not found out about the clones, then the clones would be protecting the Republic by TPM. In this case, a Jedi is doing something good that was subverted by the Sith, and yet you blame the Jedi. Furthermore, Mace and Yoda apparently believe that the clones were ordered by a Jedi (as stated by "Labyrinth of Evil") and they subsequently use those clones - who clearly aide the Jedi right off the bat - at a time when they are most needed. Even the Kaminoans believed this was for the greater good.
"Even at that, Obi-Wan and Yoda bring the army to light, and help militarize the Republic. "
So, by "stepping back and seeing what side of the battle" they are on, you mean just wait for the Separatists to invade the Republic, with a perfectly good and biologically obedient army just standing by?
Everyone thought they were doing the right thing. Nobody knew that Palps was orchestrating such a grand scheme, and yet you are laying a tremendous amount of blame on them. In fact, you accuse them of doing nothing, and yet criticize everything they do. Exactly how successful do you expect yourself to be against a person who can forsee the future and use powers of the Force against you?