My goal is to find out how many files are there whose extension doesn't match the real format.
Without opening individual images in the internal image viewer, is there a quick way to tell if the extension matches the real format? Is there a column in the Details View that shows the real format? Or is there a batch process to fix the wrong extension?
The Description column will show the real image format (among other info). You can't search on that, though. ("Description" in the Find panel only searches the User Description aka Comments that you manually add to files. Not the auto-generated information like this.)
For correcting extensions, this might be the easiest approach: