Making the Ring was certainly a mistake, but I think it's a mistake completely consistent with Sauron's character:
Gandalf describes Sauron's policies thus:
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he that strikes the first blow, if he strikes it hard enough, may need to strike no more
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As we know Professor Tolkien also says the following:
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it had been his virtue (and therefore also the cause of his fall, and of his relapse) that he loved order and coordination, and disliked all confusion and wasteful friction
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Given Sauron's nature, I think that such a "master plan", while certainly a miscalculation, was one he was practically bound to make, especially when coupled with his inability to comprehend the motives of good and altruistic people. This characteristic I think is another byproduct of his obsession with order, as his belief in the fundamental truth and logic of his own worldview made him incapable of believing that anyone could perceive the world differently.