As I recall, the President graduated magna cum laude from Harvard Law School. That means his grades had to be quite high.
His membership on The Harvard Law Review -- and his presidency there -- are not, however, necessarily indicia of high grades.
As for the presidency of the Review: I was not a member of the Review at the time Obama ran for president (presidential elections are held in February of one's second year of law school/first year on the Review), but what I was told the next year was that Obama became president of the Review because, on the final round of voting (which went on all day, traditionally, eliminating candidates in rounds), the Review's conservatives in effect decided that he was the "least bad" of the remaining alternatives. In my experience, that meant he at least gave the conservatives a hearing before he decided against them, rather than simply ignoring or actively denigrating them. Winning the Review presidency was not necessarily being recognized as the journal's most skilled or hard-working editor; one exceptionally talented and diligent editor the next year was denied the presidency based in part on specious concerns about his "insensitivity" (code for principled conservatism).
As for membership on the Review: To become an editor of The Harvard Law Review after one's first year of law school (as the President did), one had to take a week-long writing competition. This consisted both of an article to be edited (in which mistakes had deliberately been made; scores were assigned based on how many mistakes were caught and the quality of the editing) and a sample case comment, to be written with the assistance of a pile of research that had been provided.
First-years won places on the Review (for their second and third years) in several ways: First, a membership offer could be based on a score consisting of a combination of 70% of one's score on the writing comp plus 30% of one's first-year grades. Second, it could be based on a score based 30% on one's score on the writing comp plus 70% first-year grades. Third -- for ethnic/racial minorities only -- one could be selected as part of the Review's affirmative action program. No one knew exactly who the affirmative action members were (or exactly how they were chosen). My understanding is that their grades and comp scores were immaterial; the Review president and treasurer had virtually unfettered discretion to choose any minority who had taken the writing comp.
What would be interesting about the President's transcripts wouldn't be the grades; as I mentioned above, to graduate magna, the grades had to be quite high. What would be interesting is to see (a) what classes he took and (b) with what professors. The President cultivated friendships with many of the law school's professors (and, so I was told, often made a big show of calling them by their first names in class). Did he take rigorous, larger classes with blind grading (like Antitrust with Phillip Areeda or Corporate Finance with Lucian Bebchuk) or did he take seminars with his friends like Charles Ogletree on "softer" subjects, where grading couldn't have been blind because of the class' small size?
(In the interests of full disclosure, I did take some "softer" seminars -- like "Law and Literature" in the last semester of my third year -- with great pleasure. And no, I did not graduate magna.)