I can't write to my flash drive, and it is already in the MS-DOS (FAT) Format. Why?

This is my first question on this website. I am using a Mac Air, and I have a flash drive in which I can read from. I am able to copy files from this onto my Desktop, or anywhere on my computer for that matter. I cannot write to my flash drive, however. I know this is a common problem for some people. I looked into their solutions. There is one difference between the cases I've found, and my case. The flash drive's format is normally a 'NT' format, which is a Window format from my understanding.

My flash drive is formatted in 'MS-DOS (FAT)' according to Disk Utility and the 'Get Info' window from Finder. It did tell me I had removed it wrongly before. I am not sure how to fix the flash drive. Do I reformat it? If so, how and what do I format it to. Please let me know.

Thank you in advance for your help, ~Rane

Screenshot:

I do have the flash drive selected in the Disk Utility picture.

If you don't need to use this USB disk on a Windows machine, format using Mac OS Extended (Journaled). Should you need to exchange files with Windows machines, then Format as you have with MS-DOS (FAT). ExFAT should work as well.

It is not outside the bounds of possibility that the drive itself has gotten zapped somehow and is damaged, thus not operating correctly. Copy all the files from the flash drive to a folder, reformat with MS-DOS (FAT), then see what happens when you copy back. If it doesn't work, chuck it. Since flash drives are so inexpensive now, get a few more of them in larger capacities.

Lastly, (above) some flashdrives have a physical write-lock (read-only) hardware switch. If your flash drive has such a switch, perhaps it is locked? OS X does not allow the usual file & directory permission on MS-DOS (FAT) disks, so you can't try to make it read/write.

There is also a 4GB limit on a single file in MS-DOS (FAT).

So, here's what I did after much face-palming and cursing of Apple and their absolute disregard for their users:

From the terminal:

1. Identify your USB by NAME and IDENTIFIER:

diskutil list

Output is:

/dev/disk3 (external, physical):  
#:                       TYPE NAME                    SIZE    IDENTIFIER  
0:               FDisk_partition_scheme              *2.0 GB     disk3
1:                 DOS_FAT_32 MIXTAPE                 2.0 GB   disk3s1

In this case, NAME=MIXTAPE and the IDENTIFIER=/dev/disk3s1

2. Now unmount the USB:

sudo diskutil unmount /dev/$IDENTIFIER

Example:

sudo diskutil unmount /dev/disk3s1

Output is:

Volume MIXTAPE on disk3s1 unmounted

3. Now create the Volume directory - this appears to be the key!

sudo mkdir /Volumes/$NAME

Example:

sudo mkdir /Volumes/MIXTAPE

No output.

4. Now mount the USB to the Volume:

sudo mount -w -t msdos /dev/disk3s1 /Volumes/$NAME

Example:

sudo mount -w -t msdos /dev/disk3s1 /Volumes/MIXTAPE

No output.

5. Validate that the USB is now writeable:

touch /Volumes/$NAME/tmp.txt

Example:

touch /Volumes/MIXTAPE/tmp.txt

6. You should now be able to see that you were able to create the tmp.txt file on your USB in the Finder app or by:

ls -al /Volumes/$NAME

Example:

ls -al /Volumes/MIXTAPE