Because the target is displayed as a small square, and because it is often in the same area as objects that are the subject of the camera, it can be hard to select by clicking. Select the camera object, right-click, then choose Select Target from the Tools 1 (upper-left) quadrant of the quad menu. You can also choose Cameras from the Selection Filters list on the toolbar, and then click the target.
Also, if you rotate a Target camera to a nearly vertical position, either up or down, 3ds Max must flip the Camera view to prevent the up-vector from becoming undefined. If you need a camera to look vertically upward or downward, use a Free camera.