It can be more difficult for jurors to arrive at a guilty verdict when the defendant is a celebrity, but less when the defendant is an elected official. Putting aside the fact that public figures can usually afford the best attorneys available to defend them, whereas most "common" criminals are dependent upon public defenders, there is often a risk that jurors will be too enamored of the celebrity to want to believe that he or she can be guilty of a heinous crime. Unlike celebrities, elected officials on trial for corruption or worse often have the opposite problem: jurors are more inclined to want to believe them guilty because public perceptions of politicians is often very low.
The more well known the public figure, the more difficult it can be to identify potential jurors who do not harbor some underlying bias for or against such an individual.
Jurors are expected to be completely impartial, and to weigh carefully the evidence and testimony presented during a trial. Arriving at a verdict of guilt or innocence is a deliberative process. Preconceptions about public figures can reside deep within the subconscience, though, and can figure in the outcome of a trial.
In contrast to jurors, judges are usually seasoned, experienced attorneys capable of looking beyond celebrity and are also expected to be completely impartial. Honest judges who believe they may harbor grievances against a defendant or, conversely, hold a positive impression -- and the fact that many judges are elected officials themselves can color their opinion of a public figure on trial -- will recuse themselves from the case. The challenge for the judge in a trial of a public figure is to control emotions and the tendency of attorneys to attempt to sway public opinion ahead of the trial through exploitation of the media. In a highly-publicized case, the judge might impose strict restrictions on both the prosecution and the defense attorney with regard to public comments regarding the defendant.
Preventing a high-profile trial involving a public official from becoming a media circus is always difficult, but it is essential in ensuring the integrity of the judicial process.