The juicy part comes when Senators start questioning her about what sides of the cases she would’ve taken if given the chance. Then, of course, she will avoid giving an actual answer as to what she personally agreed with - something she has already done a little bit already. As Ilya points out, that's a wise strategy in terms of raw self-interest. Kagan is responding to questions by referencing to existing precedent rather than speaking about her own personal opinion. The American people won't have any concrete knowledge of her most important legal opinions, and there won't be any hiccups on her way to a smooth SCOTUS confirmation.
Another juicy part came when Sen. Sessions hit hard on Kagan’s stance on DADT, emphasizing that Kagan’s treatment of military recruiters was soley based on her attitude towards gay rights. Kagan insisted she had the utmost "honor" for the military -- direct quote -- but its would seem that she honored gay rights more than the rights of our nation's soldiers.
Lastly, Kagan said that she would be for cameras in the courtroom. Get ready for even more live coverage of legal complexities!