They can detect force adepts and others whoa are skilled at using it. In episode four, Vader is able to detect the presence of Obi wan while he's walking around the Death Star, and eventually finds him (that thing was the size of a small planet mind you). He can also tell that the "force is strong" with a certain rebel pilot in the middle of a space battle at a time in galactic history where there are no Jedi. As far as not looking for the Sith Lord, Yoda states in episode one that Sith always travel in pairs, which means they certainly had to be looking for Darth Maul's other number (and that's without even going into the Sith's goings on during the clone wars). BTW, the emperor almost certainly knew of Luke's presence on Endor, and was actively trying to trap him as well as the rest of the rebel fleet (those poor Bothans were used!).
Inconsistencies in the story? Maybe. However your analysis that they got so obsessed with winning the Clone War (mission creep) that they couldn't see the political ground shifting is spot on. They most certainly were soldiers, probably more like templars or religious order medieval knights than paid contractors. That this role superseded all other ones, and the fact that most Jedi had never even seen a Sith, much less fought one, speaks to an atrophying ability to be able to do ones own job. Cartelistic? I would say their original job was to maintain (pseudo) religious orthodoxy in the use of the Force. The fact that they had to be skilled warriors in able to do this lead to them expanding their purview to the point that they no longer had the numbers or ability to accomplish their objectives.
Big Government advocates. Meh. They clearly took advantage of the unity and structure the Republic provided, but that doesn't point to promoting Federalism. However if a planet were to encourage people to use the force outside of Jedi orthodoxy, its certain they would have tried to leverage the power of the Republic to stop it.

If I remember correctly, the Death Star was the size of a small moon, not planet. (total nitpick, I know). Obi-Wan: That's no moon. It's a space station
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One thing to add, and I'm not sure if this crosses lines of orthodoxy, but I remember in the subsequent Star Wars novels (post ROTJ), on one planet, the natives demanded that Luke adjudicate a conflict between two neighbors (I believe that one patron was demanding "Jedi Justice").
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Obi-Wan: For over a thousand generations, the Jedi knights were the guardians of peace and justice in the old Republic... before the dark times... before the empire.
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Yeah, I thought about that as I typed it. But I thought a moon was generally defined as a natural formation larger than an asteroid in orbit around a larger planet. Thus a planet can be a moon and vice verse, as long as one is orbiting something larger. That place with the Ewoks was a moon.

But you're totally right, as you pulled out the Kenobi quote. I'm pwned.

BTW: "Guardians of the old republic." Thinking about it, I know think that they only 'guarded' the Republic as long as it would help maintain the Jedi monopoly on the use of the force. They really didn't seem to care about the political landscape, and the Galactic Empire was only a threat to them when it turned out that a Sith was in charge which meant their hegemony (and existence) was threatened. (I'm only really familiar with the movies, all the novels and other canon are unknown to me).

Thoughts?

They can detect force adepts and others whoa are skilled at using it. In episode four, Vader is able to detect the presence of Obi wan while he's walking around the Death Star, and eventually finds him (that thing was the size of a small planet mind you).

He had a pretty strong personal connection with Obi-Wan, or at least he did before Mustafar. It's kind of like how Vader was able to sense Luke's presence on the shuttle whereas Palpatine couldn't.

He can also tell that the "force is strong" with a certain rebel pilot in the middle of a space battle at a time in galactic history where there are no Jedi.

That sounds more like a general saying, like "May the Force be with you" and so forth.

As far as not looking for the Sith Lord, Yoda states in episode one that Sith always travel in pairs, which means they certainly had to be looking for Darth Maul's other number (and that's without even going into the Sith's goings on during the clone wars).

They had no idea, though, that it was Palpatine. You could possibly chalk that one up to Jedi arrogance - they didn't even think that the Sith Lord might be right under their nose until it was too late.

BTW, the emperor almost certainly knew of Luke's presence on Endor, and was actively trying to trap him as well as the rest of the rebel fleet (those poor Bothans were used!).
Inconsistencies in the story? Maybe.

Palpatine actually didn't know that Luke was with the rebel group on the shuttle until Vader told him. Remember when Vader tells him that he sensed him, and Palpatine's response is something like "Strange that I did not"?

However your analysis that they got so obsessed
with winning the Clone War (mission creep) that they couldn't see the political ground shifting is spot on. They most certainly were soldiers, probably more like templars or religious order medieval knights than paid contractors.

That's certainly what they became - soldiers.

It's one of the things I really like about the prequels - the way that the Jedi Order falls into destruction. The novelization put it best when it said that the Clone Wars were always the "revenge of the Sith".