A trial would be considered too speedy if the defendant, that is, the accused, is not given enough time to adequately prepare for his or her trial.
In terms of the "public" aspect, a trial might be considered too public if spectators tried to interrupt the proceedings in the courtroom, or if testimony might be embarrassing to the people involved in the case. Not to mention the fact that too much media coverage might, in some way interfere with the judicial process.
