Potion of Invisibility / Invisibility doesn't work

When I use a potion of invisibility, mobs can still see me, look at me, follow me, attack me. (I do not wear any armor or holding anything in my hand.)

See video for example.
http://www.youtube.com/watch?v=LKXJU_ofVbs&feature=player_embedded

(Video is not from me: http://www.minecraftforum.net/topic/1869925-possible-bug-invisibility-doesnt-work/)