When criminal charges have been filed by the District Attorney who has the power to dismiss the charges?

Once formal criminal charges have been filed the only person who has the power to dismiss the charges is the District Attorneys office.
The judge does not have the power to dismiss the charges until and unless there is a preliminary hearing in a felony case or a trial in a misdemeanor case.
Even if the judge believes the case is very weak, in a misdemeanor case, the judge must allow the case to proceed to jury trial if the District Attorney demands a trial.

If a judge has found probable cause to hold the defendant to answer in a felony case then there will be a jury trial unless a plea bargain is reached or the District Attorney agrees to dismiss the charges.

This is why it is so important for your criminal defense lawyer in southern California to be very familiar with the District Attorneys in the court where your case is pending.