I can't seem to be able to reproduce these problems.
Are you using actual image planes or just Poly planes with images mapped to them? If not then try using actual image planes. This might might be a better option for you.
www.stevenegan-cgi.com
"Your weapons are no match for ours! People of Mars, surrender!"
"Um, this isn't Mars. This is Earth."
"Earth? Earth-with-nuclear-weapons Earth?"
"Yes."
[long pause] "Friend!!"