Magnum shows the ice cream shop owner a picture with Mac in it, with Mac being on the right side of the photograph. Magnum then goes next door to another business and pulls out the photo and asks the owner if he recognizes Mac, but states "on the left".
When Magnum first tails Mac from the ice cream shop, it's during the afternoon. As Magnum follows him closer and finally finds him in an alley, it's night time.
When Magnum is talking to "Mac" on the beach, Higgins is watching him through a pair of binoculars. However, in subsequent shots, Magnum is sitting with a fence and large bushes behind him, making it impossible for Higgins to actually see him.
In the opening scene just as Magnum puts on the reflective sunglasses, for an instant, you can see the camera and cameraman reflected in them.