Audit trail numbering system has gaps and is not continuous for monitoring all transactions entered.
What accounts for the numbering gaps? Is there a continuous numbering system somewhere to control all
entries to the system?

All transactions are numbered, but the audit trail only shows transactions that have been edited or deleted after initial entry. If an entry was made, but never modified, it won't be listed on the audit trail.

If you want to see a list of all transactions, with their number, choose a transaction report (Accountant/Taxes or Custom), select All for all fields. Modify the report & on the Display tab, check the Trans #. You can also select the Entered/Last Modified & Modified By columns. If you want them in transaction number, use the Sort By field.