Just as Jack says, "On deck, you scabrous dogs," to the very left edge of the screen over Jack's shoulder is a grip crew member with a tan cowboy hat, white short sleeve tee shirt and sunglasses, just standing there looking out to sea.
When Neo is going to open the door to enter the Oracle's house, you can clearly see a camera on the doorknob. There's a sheet over it painted to look like the wall behind it, with a representation of Morpheus' tie too, because he's blocked by the camera.
During the scene when Dorothy and Scarecrow are fighting with the trees, Scarecrow says "I'll show you how to get apples" and he gets hit by the apples. The very next scene if you quickly look at Dorothy's shoes, you can see that she is wearing black shoes, not her ruby slippers.
Right after they "create" Leeloo and she is lying in the plastic cage with the little straps on her, the guy approaches her and says, "if you want out, you are going to have to work on your communication skills." She gives him a dirty look, and then you can see a huge hole, pre-cut in the glass, that she busts her hand through.
During the honeymoon sequence at the end of the film, if you look at the right top of the flowers in the vase during the "flowers covering nipples" bit, you can see a bit of red duct tape covering Liz Hurley's nipple from behind the flowers.