Give an example where local political considerations somehow influenced the outcome of a criminal trial.

Prosecutors in most parts of the United States are either
in elected positions, or they are interested in someday seeking one, such as a District
Judge or the like.  So in that way, many, many cases are either pursued or prosecuted
with different amounts of zeal because, whatever the legal considerations, the outcome
will affect popular opinion and therefore elections.

Take,
for example, the trial of Byron De La Beckwith in Mississippi, on two occasions in the
1960s for the murder of civil rights leader Medgar Evars.  In one of the trials, the
former Governor of the state, Ross Barnett, entered the courtroom, while Evars widow was
on the stand, and shook hands with Beckwith in front of the jury.  The trial resulted in
a hung jury.