How do you resolve database inconsistencies

Inconsistent database?

The history:
Synchronization of iPhone via ActiveSync protocol with Exchange Server 2003 SP2 (on a Windows Server 2003 Enerprise SP2). Works smoothly.
My boss wanted a certain public calendar to be synced with his private calendar so that he could update and edit it on his iPhone and iPad.
The ExchangeSync tool (version 2.1.7) was obtained from CodeTwo. Due to incorrect installation instructions, this caused certain authorizations to be set and calendar entries to be created multiple times.
This means that this problem only occurs with series elements. ExchangeSync tries to synchronize the entries and due to an error this fails and it creates a kind of zombie entries. This means that the entries already refer to a series element, but then again not.

Well, now the real problem:
A colleague from development built me ​​a tool with which I can automatically remove these multiple copies from the public calendar. This works via the OWA. This tool examines the multiple copies and looks which of them was created first and deletes the rest.
The problem with this is that only the faulty series elements are deleted and not the entire series.

Now the following happened yesterday: I wanted to clean up our public calendar (with a user who has full access to the administrative permissions) and an error occurred with some entries. When I want to look at these files I get the message "Client operation failed"
I was once so free and activated drive M: with a registry entry to check whether the calendar entries could possibly be deleted via it. This is also not possible. The error message "NAME OF CALENDAR ENTRY cannot be deleted: The specified path could not be found. Make sure that the path is correct." appears.

In fact, these multiple entries can no longer be deleted.

To me it looks like the database is inconsistent. There are elements that no longer exist, but are only displayed without any information behind them.

PFDAVAdmin also tells me that of about 7500 elements in this public calendar 54 no longer have any item leverl perms. I think these are those entries that I can no longer delete.

I am at a loss and just don't know what to do next. Maybe someone of you can help me.

Our systemspecs:

Exchange Server:
Windows Server 2003 Enterprise SP2 32 BIT
3.5 GB of RAM
Exchange Server 2003 (Version 6.5 (Build 7638.2: Service Pack 2)

The server on which ExchangeSync is running:
Windows Server 2008 Enterprise SP2 64BIT
48 GB RAM (HyperV host)

Do you think an offline defragmentation of the DB would help to remove these inconsistencies? Could it also be authorization problems?

With best regards