For each FTP filesystem you have mounted, a log file is kept of the most recent Synchronize, Put All, and Get All operations.
(See Troubleshooting Tips for a way to remove the log files from your Filesystems display.)
Click on the Runtime tab, then click on the plus sign (+) next to the FTP Filesystems node.
Next, double click on the plus sign next to the FTP filesystem whose logs you are interested in.
Lastly, double click on the log you want to view. The log is displayed in the Output pane below the Runtime pane.