The point of this question is about how double-jeopardy could potentially be abused.
Say that Bob is suspected of murdering Mary. If he is tried for this crime and found not guilty, then he can't be tried again for this case due to Double Jeopardy (if I'm not mistaken).
But what if Ivan the Incompetent was in charge of the prosecution for Bob when Bob ended up walking free. Any other prosecutor would've handily had Bob behind bars, but Ivan was just a complete idiot who happened to file the case first. Is any other party not allowed to take Bob to court about this afterwards simply because Ivan the Incompetent got to it first?
A mildly related example to consider would be Bill Cosby's case, where seemingly incompetent mishandling of the case resulted in his release, whereas a more proper team would have probably easily gotten him convicted.
Lastly, a question about abuse: what's stopping Bob from asking his friend Ivan the Incompetent to prosecute Bob for his crime and do a terrible job at it, so that Bob ends up getting off innocent and can no longer be prosecuted over it due to double Jeopardy?
Edit: Can someone get protection under Double Jeopardy for a crime by arranging to be put on trial with fake evidence that is then disproven? seems relevant. But note that I'm asking in particular about whether a very poor prosecution can leave one innocent for life of a particular crime. For example, if Charlie is poor and hires a bad lawyer to prosecute, and loses. But his brother Dave, who's rich and has good lawyers, also wants to prosecute Bob. Is Dave just out of luck because of Double Jeopardy?