UPDATE: John Lynch, in the comments, has, to my mind, refuted the concerns about publications (a Lecturer is not expected to publish, nor is the Harvard Law Review President), but my main concern was about the false statements. Two of the false statements are that he claimed to have "passed laws" that "extended healthcare for wounded troops who'd been neglected" when he didn't vote on the bill in question, and his statement that "Just this past week, we passed out of the U.S. Senate Banking Committee--which is my committee--a bill to call for divestment from Iran as a way of ratcheting up the pressure to ensure that they don't obtain a nuclear weapon" when he's not even on the Senate Banking Committee.
On the latter point, Obama's campaign says he meant to say "my bill" rather than "my committee," in which case the statement becomes somewhat more accurate, as Obama did supply some of the provisions to the bill in question. But it isn't really Obama's bill, despite his contributions. It's more accurately described as Christopher Dodd and Richard Shelby's bill.