Mine, like a lot of others will not show the first dot when full or it will disappears quickly. I talk to a Nissan service manager about it when I was having some work done and he said the part $300 before labor and that there was no guarantees that it would work any better than the one I have, so I just live with it.
Yup, the fuel gauge is another one of those little annoying things with the 370z that Nissan knows about, but does nothing.