I had similar symptoms to barnabasnagy and they were caused by the Style Sheet not loading – search your page source for “wp-super-popup/colorbox.css” to see if it’s the same cause.
I’m only a 2 day old user, and we’ve tested in FF, IE(8), Safari (PC & iPad) & Chrome and it appears OK to us.
I’ve tweaked it to become a popup on demand, but if I’ve tweaked properly that shouldn’t impact the fundamental workingness (should it?).
Anyway, FYI, here’s our implementation running on a Google Places eCourse Landing Page… (click the “Contact Me” button to pop the form).