As already said I have a few ideas to make the properties dialog better. I have found a little time to finish the first part. In the attachments is an example graphic which shows the changes.
In my opinion using checkboxes to show the permissions are the most easiest way to understand them. I have even split the execution flag for files and directories to avoid problems if somebody want to make recursive changes. This means on recursive changes directories are only getting the Access flag and files are only getting the Execute flag. This way somebody can easily give all his directories and files read and write permissions without making all files executable but be able to access all directories.
If only files are selected and the properties dialog is opened theoretically the Access row isn't needed. But in my opinion the row shouldn't be hidden instead all checkboxes should be unchecked and greyed out so that they are not clickable. If a directory is selected all rows should still be shown.
The behavior how the changes are recursively taken should be still the same as it currently is.
Just say me what you think about this changes. If they are fine I will continue with the second part.