There's clearly plenty of opportunity for someone to score political points with this case.

• Declaring Knox guilty and in need of extradition which will likely be denied, will make it easier to reject extradition requests from the US, and will have an effect on national public opinion, probably an increase in nationalism in both countries.
• Declaring her innocent will be seen at least somewhat as bowing to US pressure and/or acknowledging that the criticism of the Italian justice system was accurate.
• This case helps Americans remember that Italy exists.
• Politicians sometimes like distractions, and this is a good example. They need to coordinate either the thing to be distracted from with the case, or the case with the thing to be distracted from.

There's a few more effects, but I suppose the main question is whether the Italian justice system likes to play politics.