jDownloads 3.2.39 doesn't seem to handle correctly the uploading of files with uppercased extensions, such as foo.PDF, either in the backend or frontend.
1. In the backend, the list of allowed extensions is lowercased before checking against the extension of the file to be uploaded, so something like foo.PDF will never be matched.
I've attached a possible patch for administrator/components/com_jdownloads/controllers/uploads.php (uploads.php-patch.txt). (Actually the first part of the patch is just to stop php warnings that COM_MEDIA_DEBUG is undefined on line 62 of uploads.php.)
2. In the frontend uploader, the file extension images in images/jdownloads/fileimages/ all have lowercase names, so foo.PDF won't be given the correct image. Also, for consistency with the backend, presumably the list of allowed extensions should be lowercased before checking.
I've attached a possible patch for administrator/components/com_jdownloads/tables/download.php (download.php-patch.txt).