The problems we are asked to fix
They fall into a small number of recognisable categories, and each has a defined remedy.
Court permission where a case is pending
A pending prosecution does not automatically disqualify you from holding a passport. The practical route is an application to the court where the case is pending, seeking permission for issue or renewal and, separately, permission to travel abroad for a defined period.
Courts routinely grant these where the accused has been regular in attendance, on conditions such as an undertaking to return by a fixed date and to appear on the hearing dates. What matters is that the application sets out the purpose, the itinerary and the conditions the applicant is prepared to accept.
Getting a namesake or stale record corrected
A surprising proportion of adverse verifications come from an old case against someone with a similar name, or a matter that ended years ago but was never updated. The fix is documentary: certified copies of the closure or acquittal, an affidavit, and a representation to the passport office and the police.
Do this before the next application rather than after, because once a refusal is recorded it takes longer to unwind than the underlying error ever justified.