Mouse control of a camera in an OpenGL program
Is the camera a global entity?  Will the only ever be just one?

Perhaps, but perhaps not. You can have two or more viewpoints shown in multiple viewports.  You might use shadow mapping, which positions a camera at a light source for rendering a shadow map.

If you are thinking of a generic “mouse controller” for a camera, which you can reuse in multiple applications, I’d shy away from the global camera. 

If you are working on a one of a kind application, have no intention of reusing the code, will only ever use one point-of-view, and needs the minuscule speed gain and reduction of complexity of not passing a pointer to the camera around to functions as required, a global camera is fine.