Facebook passwords are NOT case sensitive
Of course it's 'by design' so they don't have to deal with Caps Lock support issues. If I had a £1 for every support call I ever fielded where the caller had Caps Lock on during my career I'd have been able to afford a nice little vacation somewhere. It's why I spent time writing and implementing Group Policy Objects in Active Directory for complex passwords when I did Network Admin so clients' users would actually have to THINK first before typing so critcal issue calls got through 1st time and could be dealt with promptly on a Monday morning instead.
Though have you noticed that if you just type any nonsense characters into the Fb password box (my baby frequently tries to help me log in) and hit Enter it does ask you to check if you have Caps Lock on..!