This one leaves me genuinely torn. On the one hand, let's face it--this is the episode where the Sensorites seem to pick up the Idiot Ball and really run with it. In order for the Doctor to be the hero of the story, he has to make a lot of deductions that have utterly eluded the Sensorites in a very short span of time. He figures out that the water is toxic because Ian was the only one who drank from it; he figures out that the poisoning only happens in one district at a time, and that the reservoirs and not the aqueduct must be the cause. He tests the water, he finds the antidote, and he figures out that the fact that the aqueduct is shrouded in darkness and full of things making loud noises is not a coincidence, but a ruse to drive the Sensorites away. For him to do all this in the course of a half-hour (even with the aid of a "SCIENCE!" montage) makes the Sensorites look foolish indeed.
And then there's the City Administrator. Not only has he irrationally seized on the idea that the Doctor is EVIL! and must be stopped, but his logic involves believing that the Doctor has entered into an elaborate ruse to distribute poison to people who are dying anyway for Reasons. Oh yes, and if he gets into his TARDIS, he'll come back with a fleet of spacecraft and soldiers to enslave the entire planet. And the City's Administrator's grand plan, his big, shocking, utterly twisty scheme with which he will undo the EVIL Doctor...hinges on realizing that all the Sensorites look alike without their sashes. This seems like one of the most crazy dumb plans in the history of Doctor Who, an unopposed sprint to the end zone of stupidity with the Idiot Ball grasped firmly in both hands.
The real truth is that people don't always react sensibly in a crisis. They don't always do the expected thing, they don't always act in a reasonable fashion, and they sometimes fall victim to blind spots in their perception of the process. Of course the Sensorites don't think it's the water--they tested the water and found it to be free of contamination. They didn't think to retest it, or test it at different locations, because they assumed that it was a natural phenomenon and thus a consistent one. The Doctor's breakthrough is in the way he reframes the problem by considering deliberate intent, allowing the scientists to find a solution. And of course, since he's assuming that someone's trying to poison the water supply, all of the seemingly disconnected events at the aqueduct fit an obvious pattern to him. (His decision to wander alone and unarmed into a situation where saboteurs are trying to kill thousands of people, on the other hand, could be a pretty big grab at the Idiot Ball.)
And the City Administrator's actions...while they don't make sense, they don't make sense in a very sensible way. His fears of an army of humans coming to enslave the populace and exploit all the natural resources is, let's face it, not exactly without justification given our history and the fact that the last two groups of people to come to the planet have wanted to enslave the populace and exploit all the natural resources. Once you start with that fear in your heart, it's easy to let paranoia carry you into developing all sorts of crazy conspiracy theories that don't make sense. Xenophobia and cognitive dissonance do most of the work once you start with the baseline assumption that any human-like being hides hatred in their closed and suspicious minds.
And yes, the idea of impersonating the Second Elder by stealing his sash is presented absurdly ("I had never thought of that!") but his later explanation makes it sound better. He's not just saying that all the Sensorites look alike; he's saying that all but a few Sensorites have never seen their leaders close at hand, and that they're used to obeying the symbols of office more than the individuals. It's no different from dressing up as a sergeant and expecting to be able to boss around privates. When you stop trying to think of it as a story and start trying to think of it as the realistic response of a society undergoing a crisis (actually two crises, one cultural and one of public health) it starts to feel surprisingly textured and intelligent. The characters might be idiots, but they're idiots for genuine and realistic reasons, not writerly fiat. Basically, they're Idiots without any Balls.