What is the purpose of records in the ticket system? I can think of two:
To provide a complete history of what happened all in one place.
To provide a clean record of the problem and solution, e.g. your ticket system is also your knowledge base.
Deciding which of these goals is more important should inform your approach to editing.
If you support editing you should do it in a way that doesn't lose data that you would want for auditing. Whether you make the revision history available to your users, or only to admins of some sort, depends on how your users use the system: should they simply operate on the current state without regard to what happened along the way (think 911 dispatch), or should they have access to all the history to provide a better solution (think software-bug-tracking system)?