You can get individual log files for each frame:

1. In the Arnold Render Settings, go to the Diagnostics tab.
2. In the Verbosity Level list, click Warnings + Info.
3. Click the File check box.
4. Click the folder icon and choose a folder for the Arnold log files.

Or you can check the MayaRender log, which will be one log file, with the log messages for every frame.

On OSX, open the Console and look for ~/Library/Logs/Maya/mayaRender.log