If you are talking about JPEG files, then the utility jpeginfo is exactly what you're looking for. It can check files for different types of JPEG errors and corruption and either return an error code (the most useful thing for scripting), or just delete files with errors.

I use this as part of my initial file transfer, to make sure everything copied okay without relying on manual checking. (After that, I make sure their checksums don't change as part of my normal backup/bitrot protection.)

The program is command-line, and comes as source code, but it should be easy to build and use on any Linux distribution or on a Mac with a development environment set up properly. I'm sure you could even do it on Windows with Cygwin or MinGW. (For example, although I can't vouch for its integrity, this blog post seems legit and includes a precompiled download.) To build it yourself:

$ git clone https://github.com/tjko/jpeginfo.git
Cloning into 'jpeginfo'...
[...]
Checking connectivity... done
$ cd jpeginfo/
$ ./configure && make

This should create a jpeginfo command which you can either run in place or copy wherever you want (possibly using make install).

Then, you run it like this:

$ ./jpeginfo -c *.jpg
test1.jpg 1996 x 2554 24bit Exif  P 6582168  [OK]
test2.jpg 1996 x 2554 24bit Exif  P 6582116  Premature end of JPEG file  [WARNING]
test3.jpg  Corrupt JPEG data: 1 extraneous bytes before marker 0xe2 1996 x 2554 24bit Exif  P 6582169  [WARNING]

Here, test1.jpg is perfectly fine, and test2.jpg I deleted a few bytes from the end, and test3.jpg I changed some random bytes in the header.

If you have RAW files, check out this page from the American Society of Media Photographers on DNG Validation, or one on data validation details, which covers using Adobe's DNG converter to batch-validate proprietary RAW formats. (Unfortunately, this is a GUI operation and not necessarily easily scriptable.)

If you have a camera which natively outputs the 1.2 version of DNG, that's even better, as this includes a built-in MD5 checksum of the image data. Unfortunately, this doesn't seem to be stored with the normal image metadata — or at least exiftool and exiv2 don't recognize it, and they do read 1.2 DNG files in general — which means that as far as I know currently the Adobe validation tool is the only way to take advantage of that too.