I would suggest that letting the banking/financial system collapse is a mistake, and that Lehman was too interconnected to fail. However, prior to the failure of Lehman, there was no consensus regarding when and how to intervene. Paulson and Bernake intervened in BSC and wiped out the stock holders but saved the debt and counter parties. They intervened in the GSE's and saved the debt, but blew up the equity and preferred shareholders (which had the knock on effect of evaporating a lot of bank capital).
All the while, there were huge arguments regarding moral hazard, free markets, the beneficial effects of failure, etc. There was no political consensus to save the financial system from collapse. There was a lot of denial and enough ideology being tossed around to choke a horse. The quasi religious belief in markets was hanging tough.
In fact, we needed a bright line -- a watershed event that would demonstrate the need for massive intervention. Any intervention that worked had the disadvantage of failing to prove it was needed. One could always argue that Bear Stearns would have worked out just fine if we had just let the markets deal with its failure. Ditto for the GSE's, Countrywide, etc.
We had to have evidence of sufficient urgency and severity in the financial system's problems. Something had to fail with severe consequences -- or else the argument that subsidizing/rewarding failure is always a mistake could not be addressed with anything but theoretical arguments.
In a sense, Lehman was perfect, since it was big enough and interconnected enough that its failure was costly. But not fatal. After Lehman, McCain could no longer say the economy is fundamentally healthy. No politician could argue that the only thing the economy needs is less government -- at least in a serious manner.
Something spectacular needed to happen to provide the basis for supporting a bailout. People needed their "come to Jesus" moment. And they got it.
Killing a canary wasn't enough, but you didn't want to blow up the system. Enough of a taste of the "creative destruction" of capitalism to make the prospects of a painful cure seem better then letting the disease run its course.
So, it wasn't a mistake. Maybe not optimal, but letting AIG or C fail would have been much, much worse. Ideally one would want enough intervention to allow an orderly unwind of excesses. But to develop political support, especially in the face of strong ideologically motivated opponents, required a shock. That was Lehman.