It might not be the format of the drive – but some of the files on it.
When the Finder copies files to a volume with a non-Mac filesystem (like FAT32), it may create extra directories and files whose names begin with '.' to keep track of various things. For instance, if your iTunes/Music Library contained a couple of songs called SONG1.AAC and SONG2.MP3, and you copied those to a flash drive, the drive might get
SONG1.AAC
._SONG1.AAC
SONG2.MP3
._SONG2.MP3
The files whose names begin with ._ are not AAC or MP3 files. They contain (or are placeholders for) metadata that Mac filesystems have, and FAT32 doesn't. On a Mac, the "._" files are invisible in the Finder, since a leading "." is an old Unix convention for hiding a file from "regular" directory listings.
But a car stereo or digital photo frame may see a file like ._SONG2.MP3 or ._PHOTO3.JPG, assume that it contains a song or a photo (based on the file extension), then complain loudly when it discovers that the file is "corrupt."
One way of dealing with this: Just before ejecting a USB drive, go into Terminal and type
dot_clean -m
Put a space after that, but do NOT hit RETURN. Drag-and-drop the USB drive's icon from Finder into the Terminal window. That will complete the command line by typing in the Unix file path corresponding to the USB drive. Then hit RETURN. Following that, eject the drive from the Finder before the Finder has a chance to create more "._" files.