You can securely read MOVEit Central's tamper-evident task run, transfer and audit database directly with SQL commands issued through an SSL connection established by MOVEit Central API. If you have local access to MOVEit Central or the security of the connection to the database is not an issue, ODBC access can also be used instead of MOVEit Central API.
Please also see the "Database - Schema" documentation.
You can also "tail" the MOVEit Central log file, usually written to the same folder into which MOVEit Central is installed. Configuration options for the log file are found in the System Settings dialog through MOVEit Central Admin. The amount of detail written into the log is controlled by the "Global Debug Level" on the same dialog.