I do not use Invisihield but I do use the Anti-Glare screen protector. It eliminates the "water/oil spots" for me. Not sure if the Invisishield is thicker or not but the Ant-Glare is fairly thick.
I do not have any probs typing. The only thing that I have noticed is that it is easier to type in Landscape Mode while in the Otterbox. The raised beezel makes hitting the "P" and the "Q" hard for my fat thumbs when in Portrait Maode.

When I am in Landscape Mode I have no probs at all. I am actually quite fast.
Only thing that I can think of is to be sure that the Otterbox is "snapped" together. You need to hear it click at all three locations. I always have to double check that myself for that.
