His full remarks for those who missed them and have 49 minutes to spare:

Matt Latimer spells out why Clinton soared:

For all of his tortured arguments and wonky, ponderous asides, Bill Clinton made a substantive case. He dealt with facts and statistics.  He made points and then explained why he made them.  He had details. Boy, did he have details. In short, he did what almost no one at the Republican convention tried to do, what few conventions bother to do anymore.  He treated the American people like thinking human beings.

Larison adds:

 [H]e gave the sort of speech that Ryanmaniacs might have once imagined that Ryan would deliver and the sort that some Romney supporters still imagine Romney is capable of giving. Romney-Ryan was supposed to be the presidential ticket of the "data-driven" manager and his budget wonk sidekick, and between the absence of any significant policy discussion last week and what happened tonight that has lost all credibility. 

Ryan Lizza calls Clinton "the ideal spokesman to appeal to those skeptical former Obama voters that his campaign is trying to win back":

This was the anti-Michelle speech. While she naturally gave personal testimony about Barack Obama’s character and urged voters to support him on that basis, in the story Clinton told Obama was an ephemeral figure. There were few personal details or anecdotes about the President because Clinton isn’t particularly close to Obama. It was a speech about facts and three and a half years of decisions made and outcomes achieved. By the end of it, the only logical conclusion, Clinton argued, is that Obama would do a better job than the alternative.

Alex Castellanos claims the speech "will be the moment that probably reelected Barack Obama." Jonathan Bernstein counters:

A quick caveat is necessary about the effects of the speech. No, it’s not going to suddenly make voters run out and vote for Barack Obama; I don’t know how to judge these things, but I sort of doubt that it was as good at energizing Democrats as Michelle Obama’s excellent effort last night. On the other hand, you’re going to hear some silly analysis about Clinton’s speech somehow or another hurting Obama. That’s nonsense.

Suderman fact-checks Clinton:

On Medicare, for example, he argued that ObamaCare’s Medicare cuts extend the solvency of Medicare — which, as I noted recently, is only true if you double count the savings, using them to pay for both an extension of Medicare’s trust fund and ObamaCare’s new insurance subsidies. He went after Mitt Romney’s campaign for attacking the Obama administration’s assertion of new, legally dubious authority to grant waivers to welfare’s work requirements. “The requirement was for more work, not less,” he said. Not wrong, exactly, but not the best truth. The requirement was to move 20 percent more people from welfare to work — and an easy way to do that is to increase the program’s rolls, thereby increasing the number of people who successfully move on from the program. He bragged about the higher number of jobs created by Democratic presidents, a comparison that, as Ron Bailey [noted] last night, is less favorable depending on how you perform the count.

Noah Millman, who downplayed the speech before delivery, eats his words:

 [W]hat I’m most impressed by is that Clinton really did seem like the elder statesman of the party. He’s replaced Ted Kennedy. This speech was “about him” only in the sense that you could never forget who was giving the speech. Clinton himself never became a distraction.

Jonathan Cohn pinpoints Clinton's strongest arguments:

You can take real issue with Clinton’s claim that Obama did all that he could to create jobs. You can't really argue that Romney, who’s never put forward a plan for short-term job growth, would do more. You can quibble with Clinton’s suggestion that Obama has focused enough on the deficit. You can’t really suggest Romney, whose own budget plan is the stuff of fantasy, is more serious about it. You can disagree with Clinton’s argument that Obama has reached across the aisle. You can’t suggest, with a straight face, that Romney and the Republicans ever had the slightest interest in compromise.

Cassidy thought the speech a tad long:

At half the length, or a bit shorter, Clinton’s speech would have been extremely effective. Even as it was, it was certainly memorable. … Clinton went on, and on. By the end, he sounded a bit like an insurance salesman who has been invited into the parlor to describe his policies and who refuses to leave.

Just how much did Clinton ad lib? This much:

Bill Clinton’s prepared remarks: 3,136 words. Bill Clinton’s remarks as delivered: 5,895 words (counting audience cheers).