The growing influence of the Dark Side of the Force interfered with their ability to do their job
Running a military doesn't require Jedi precognition. It does require a whole lot of people to populate your military, fly the spaceships, fire the guns, etc. They don't have to be Jedi. You'd need a small number of Jedi running a military of millions or billions of recruits.
How did the Dark Side stop the Jedi from knowing they need to do all that once they realized they were in a war, and then doing it? Normal people can do that kind of thing.
And the civilians of the Republic must have been incredibly complacent just to leave everything up to the Jedi. When the Jedi were caught napping, I'd have thought there would be a popular outcry for them to be removed from military command, due to incompetence.
I really cannot fathom how either the Jedi or Palps keep their jobs.

I figure nobody in the Republic is actually paying attention to what they've been getting up to.
As a politician he was fully aware of all the inner workings of the Republic, knew how weak and decadent it was along and exploited those weaknesses.
I'm still waiting for the Republic to be
portrayed as weak and decadent. It seems to be in some ways. Using a clone army is wrong; Palps and the Jedi are screwing up royally and nobody is paying attention (maybe they don't care); the Jedi claim to care about the people of the Republic but then we run across cases like Boba where it's all just talk. However, I'm still not sure that I'm meant to see all these things or if it's just careless writing.
From Shaak Ti's calling them "living beings" rather than "people" or something similarly humanizing, my guess is the Jedi think of them as animals.
Could be, but that's another ambiguous case. I'd just like something definite - the Republic is rotten, clones aren't regarded as equal to real people, etc.
Keep watching, there's more dirty politics and corruption coming than most people have been able to handle
Hurray! Things are looking up.
Besides, we're already very close to being able to realize the other side of the PT equation: an army of droids. We're already using robotic aerial drones in combat, and other types of military robots are in the development stages as well. That's a far more practical way to go if you want mass-produced, disposable troops.
That's the thing that gets me - a droid army stops you from having to use your own people as cannon fodder, so isn't it a good thing? Why are the bad guys the ones with the droids, then? The moral issue with droids may be that they make war sanitized for the side that uses them (assuming both sides aren't using them) but that point hasn't been part of the story so far.
But your missing the real point, which is that if Lucas disapproves of the Bush Administration's use of torture, why is he continuing to portray the Jedi's use of the clone army as noble, heroic and good? I've been waiting and waiting for the other shoe to drop, but it hasn't and I don't think it will. I think that whole analogy is yet another half-baked idea from the PT, not worth fussing over I guess.
Seriously, after the Zilo beast episode, how could anyone in ROTS be cheering when he announced that the Republic would be reorganized into the Empire? Who would possibly trust a man who decided to bring an exceptionally dangerous beast to a planet with one trillion people?
The real estate lobby must have been overjoyed at all the space for development the Zilo Beast cleared.