Paul Ryan overreached when he said Obama is responsible for shutting down a plant in Janesville that actually closed during W's presidency. He handed Democrats a great tool to show that Paul Ryan is dishonest and incompetent. Through attacking his character with this vivid example, Democrats can get Ryan's approval rating underwater.
Ryan's statements are clearly not true. Ryan should know they aren't true, given that his own office even sent out a press release about the closing.
Unlike Medicare or welfare, which are complicated systems that people have preconceptions and emotional responses to, few people outside of Janesville have a vested interest or ties to when exactly the Janesville plant closed. Most people will accept correcting Paul Ryan on this one -- even if they then make excuses for it, and intend to support Romney/Ryan anyway.
Since people will accept that Paul Ryan was wrong here, Democrats can say that his blunder is an example of a pattern in Paul Ryan's behavior as a candidate and an elected official. People love patterns based on an example they can get their mind around. This is exactly why the Bain attacks worked on Mitt Romney's approval rating.
Democrats can use Ryan's Janesville overreach in two ways:
(1) The obvious thing is to say he's a habitual liar. This could drive up his negatives in the same way as Bain did for Romney. Even Republicans don't trust him.
(2) The less obvious, but also effective thing to do would be to say Paul Ryan is not competent. What kind of "wonk" can't get basic dates right? If he and his staff are messing up simple dates, why should we trust that what he's doing with all his Medicare fuzzy math? Why should we trust that this young guy knows what he's doing? There are contexts where Democrats cannot just call Republicans liars without all hell breaking loose. The beauty of Ryan's Janesville blunder is that it can easily show that Ryan is "in over his head" and "not ready to lead." This is a species of attack that the GOP uses on Obama that tends to work with more moderate types. This type of attack may be picked up by independents and moderates who have misgivings about Ryan but don't necessarily dislike or distrust him. If voters begin to doubt Ryan's smarts and competency, that could drive down the intensity of his positives, or even cause his negatives to go up a bit.
If either of these narratives spread, it will weaken the narrative about Ryan as the guy who'll set Romney straight and provide substance. Given that the media is paying attention to Ryan's lies, Democrats should take the opportunity to spread this type of message about Ryan to weaken his contribution to the Republican ticket.
Update: I have added the link to the press release. Many thanks to COWoman for the link!