This frequently happens with secretaries of Defense, and it has been of benefit to the administrations that have done it. FDR picked a Republican, Henry Stimson, to be secretary of War in 1940, and that meant that the war — and the war's casualties — became a bipartisan matter instead of fodder for partisan attacks. President Obama retained George W. Bush's Defense secretary, Robert Gates, for most of his first term. He replaced Gates with another Republican, Chuck Hagel, in that position.
Having a Defense secretary from the other party makes war bipartisan, and reassures members of the opposition that the powers of the sword aren't being abused. Likewise, naming an attorney general from the opposite party would tend to make the administration of justice bipartisan, and would provide considerable reassurance, as Holder's tenure in office emphatically did not, that the powers of law enforcement were not being abused in service of partisan ends. In an age of all-encompassing criminal laws, and pervasive government spying, that's a big deal.
I'm not sure I want war to be bipartisan but the idea of a Republican AG would really restart any number of conversations that have stalled out or stopped due to acrimony all around.
Reynolds provides a useful capsule summary of how the position is usually filled:
…in choosing a friend, Obama was following in the footsteps of presidents going all the way back to George Washington, who named Revolutionary War comrades-in-arms to the slot. John F. Kennedy named his brother Robert to be attorney general, and Richard Nixon named his law partner, John Mitchell. In many ways, this makes sense: The attorney general of the United States is at the top of the law enforcement apparatus, and in that position, you want someone you can trust.
But while presidents may feel better having an intimate, if not a crony, in charge of law enforcement, that kind of closeness raises questions for the rest of us.