After another hour of researching and trying I finally solved the problem. As Shiro suspected it was not the rendering code that causes the problem. I tried it with models from which I know they worked for other projects and they were drawn just fine.
So I began to search for issues with the lamp model itself. With the current Blender exporter, there is no option to triangulate the model during conversion. But what I tried was to apply a triangulate modifier in Blender and then exporting it, but the result was even worse than before. Now the whole model seemed to be corrupted.
My research on the internet brought me to this bug report. According to this I tried everything again with Blender version 2.68 but this solved nothing. I continued my research on the mesh by looking specifically on the corrupted parts e.g. the right lamp. What I found was that I used linked duplicates (alt+d) to copy it from one side to the other. Also I joined all parts of the meshes together.
After playing arround a bit with the two Blender versions and making duplicates real I solved it by first making all duplicates real, selecting all the single objects, applying the scale/rotation/location and checking "export selected" and "XNA strict options" in the export settings of Blender 2.68 and then exporting.

By the way to those of you who use MonoGame: the fbx exporter of Blender 2.68 does not support the binary fbx format so the fbx file will not work with the MonoGame content pipeline. To get my fbx converted to a xnb file I used a Content converter from CodePlex and added some code to convert 3d models. I then manually put the xnb to the bin/Debug directory.

To conclude I think it was a problem with both the model/mesh and the fbx-exporter.

I hope i could help some other people too.
Thank you for your help.

After another hour of researching and trying I finally solved the problem. As Shiro suspected it was not the rendering code that causes the problem. I tried it with models from which I know they worked for other projects and they were drawn just fine.
So I began to search for issues with the lamp model itself. With the current Blender exporter, there is no option to triangulate the model during conversion. But what I tried was to apply a triangulate modifier in Blender and then exporting it, but the result was even worse than before. Now the whole model seemed to be corrupted.
My research on the internet brought me to this bug report. According to this I tried everything again with Blender version 2.68 but this solved nothing. I continued my research on the mesh by looking specifically on the corrupted parts e.g. the right lamp. What I found was that I used linked duplicates (alt+d) to copy it from one side to the other. Also I joined all parts of the meshes together.
After playing around a bit with the two Blender versions and making duplicates real I solved it by first making all duplicates real, selecting all the single objects, applying the scale/rotation/location and checking "export selected" and "XNA strict options" in the export settings of Blender 2.68 and then exporting.

By the way to those of you who use MonoGame: the fbx exporter of Blender 2.68 does not support the binary fbx format so the fbx file will not work with the MonoGame content pipeline. To get my fbx converted to a xnb file I used a Content converter from CodePlex, and added some code to convert 3d models. I then manually put the xnb to the bin/Debug directory.

To conclude I think it was a problem with both the model/mesh and the fbx-exporter.

I hope I could help some other people too.
Thank you for your help.

Note: the original Content converter from CodePlex does not seem to have an official migration project elsewhere, however this GitHub project claims to be based on the original code.