There is a log although it may not be has helpful as you'd like:
C:\ProgramData\LabTech Client\Logs (Windows 7, not sure for other OS)
Information that may be helpful -
We learned that Labtech processes the configuration items in large batches and if one record errors, it kills the whole batch (maybe 100 per batch - not sure on this).
Our biggest issue came from inactive employees. If you have an agent associated with an inactive employee it will stop the whole works in it's tracks. This is very frustrating becuase it means that when an employee is terminated your workflow has to be disable in AT, then disable in LT, then whatever else goes with that. Labtech doesn't synchronize inactive employees so there's really no real two way synchronization of the contacts. Makes extra work for us.