Currently, there is no easy way to see the full path to a file. For an image, you can click on the image name to get a preview in the bottom, and then you can click on the image preview which open us the image in a new window from where you can copy the URL out of the browser window. That is a bvit longwinded, and it should be possible to see this information from within the IMCE interface. For other files like PDFs of KMZ files, clicking on the preview initiates a download, and its a lot harder for users to find out what the full path to the file was.
Attached patch shows the path to the file just below the file preview.