Isn't prosecuting someone twice or more for the same offense in the same court putting them in double jeopardy?
In a criminal trial when jeopardy attaches, that does not by itself preclude another trial for the same offense. After jeopardy attaches and before that same state of jeopardy terminates, the accused can be said to be in continuing jeopardy.
During this phase of jeopardy, another trial is not considered in the American legal system to be a second, separate state of jeopardy, but rather a continuation of the initial jeopardy the accused was placed in during the first trial.
When a mistrial is declared due to a hung jury, jeopardy does not automatically terminate in United States courts. Therefore, the prosecution may decide to try the case all over again from the beginning without this being considered double jeopardy.
Another problem that may result in a mistrial is prosecutorial misconduct. When prosecutors commit illegal acts during a trial, or fail to act in ways that are legally required of them, such behavior may result in a mistrial. For instance, if a prosecutor misstates the law to the jury, withholds evidence that would have been beneficial to the defense, knowingly uses perjured testimony, or otherwise violates the law, the judge may declare a mistrial.
Why then does the prosecution—the side that was responsible for the mistrial—get another chance? Although this may seem unfair, the "logic" here is that the defense is the side that makes the request for a mistrial and, therefore, waives its protection against double jeopardy in this instance by that request.
These are just a couple examples of the issues that may be in play when you see someone being tried again for the same offense in the same court