OpenGL errors on AMD hardware only

I am developing an OpenGL program. It works well with Nvidia hardware (tested on gtx 550ti, gtx 780 and gtx 680 on windows and Linux). It even runs on Intel Integrated Graphics (modern Intel Atom). However, I am having a lot of problems with AMD hardware. I fixed some shader bugs but it fails anyway. I have two different notebooks with AMD graphics (and Windows 7):

• Laptop A: The program starts up and most things get rendered, but some do not. My program is using OpenGL 4.0, I have verified that this video card supports it and I have the latest drivers, but if I ask GLFW to create an OpenGL 4.0 context, it doesn't work. My solution did not provide a specific context. I am getting some shader warnings and some OpenGL errors:
  • "'layout': symbol is deprecated in the current version of GLSL
  • 'gl_': reserved built-in prefix in GLSL versions 1.10 and 1.20
  • invalid enumeration (per frame)
  • (null) (only on a few frames).
• Notebook B: This time asking for OpenGL 4.0 context fails, but I get a black screen, nothing is displayed. There is only one OpenGL error (per frame): "(null)".

I don't know how I can find the problems. Moreover, I don't have direct access to these laptops (they belong to a friend).