Weird Object Shape in Solid Mode My object behaves weirdly in Viewport's Solid Mode, it's shown like this in the Solid Mode:



But when I render the scene, it's shown well (as it should be):



It only has a Bevel modifier:



The object in the Edit Mode (Solid Mode):



Edit Mode + X-Ray Mode (in Solid Mode):



Edit Mode + X-Ray Mode (in Wireframe Mode):



How can I fix it?
Bevel modifier, when applied to the whole of complex meshes in particular,  can mess things up. To avoid this model the shape from a subdivided, 8×8, plane removing undesired vertices/edges. Bevel it, selected vertices only (it's called a vertex group), to obtain rounded corners as shown below. Extrude it when done and remove doubles. 
Use knife project with the cut through enabled for the rounded holes as the rectangular hole is the subdivided faces deleted.