Why does the geometry disappear / What can cause these problems / Why does the code work on intels card but not on ATIs ?

I haven't looked over your code, but i'll address the question.

basically, each vendor puts out their graphics drivers, these drivers might be strict, or less stricter than other drivers. they might be fine with what the docs describe as "undefined behavior". it comes down to the problem of how much the vendor cares to support and spend time on their openGL implementation, as you'll find directX is generally more reliable across different vendors. IIRC some nvidia drivers don't even mind if you handed your openGL context directX shader code. it's defiantly a problem that your program may run differently on different chipsets(particularly integrated intel being generally crap). however things are getting better, but their's still plenty of older hardware out their that might have a problem with how you are trying to do things.

Also, i'd recommend checking that the ATI card supports the openGL version you are using, it's most probable it does, but just be certain, also make sure you have the latest drivers for the card.

the question i actually wanted to ask: how would i start to debug this issue?

You chose OpenGL, so you just have to suck it up now and check each call manually if there is some error

Of course, since we are talking about ATI, it is expected that they will not return the error code at all times - you wouldn't expect ATI drivers to be as good as nVidia drivers now, would you

I've seen this behaviour on multiple ATI cards under multiple sets of official drivers. Basically, the renderer worked flawlesly on everything, Intel GMA950 not excluding, just the ATI cards were unpredictable. (and that was taking into account all info there was on their issues).

If I were you, I would just display a message along the lines of "Warning ! ATI card detected. Please insert a reliable gfx card."

As you probably guessed, ATI cards gave me a hell, some time ago...

BTW, if I had to guess, I'd check if that card of yours supports 32-bit Indices first (Yes, you'd be surprised. No, just because the gfx caps tell you it is supposed to support 32bit Indices , it does not , necessarily, have to. You are welcome ).

Do you have an access to the machine ? Can you step through the code, line by line, and see where it crashes ? Most probably, some resource (VB, IB, texture, RT, ...) didn't get created for whatever reason - majority of them, of course, unjustifiable - based on gfx Caps the drivers expose...