Continuity mistake: When James Bond is fighting underwater with an opponent, the opponent rips off James' diving mask (which is blue). Then James rips another mask off another opponent who is lying dead on the ocean floor. This dead opponent's mask is black. James puts on the black mask and then he turns around and the mask is blue again.
Factual error: Bond and Leiter are in the helicopter and as Bond tells Leiter to get the military personnel to show up for the show-down, he makes reference to "Miami Beach and Orlando Beach". Seeing as how Orlando, Florida is about 50+ miles inland, there is no such place as 'Orlando Beach'.
Other mistake: During the sequence where Bond flees the baddies during the carnival, it becomes clear that the locals made their own outfits. For a few seconds, we see a group with headpieces that read "007" - so much for "secret" agent. To add a bit of humour to the moment, a dog can be seen urinating against the passing parade.
Revealing mistake: When James Bond and Felix have found the missing plane, look at the colour of the water as the helicopter lands, it is evident that is landing in shallow water, (they are supposed to be in much deeper water with sharks swimming below them) you can see the sand below. If the helicopter had landed on deeper water, the water colour would be dark blue.
Continuity mistake: Bond swims to the beach after inspecting the underside of the Disco Valante for the first time. As he walks out onto the shore, he is carrying his fins and he is wearing a red wetsuit jacket, black shorts and has a knife scabbard attached to his right leg. In this shot it is also clear to see that he is barefoot. He tosses the fins aside and unzips his jacket to remove it. After a quick edit he is tossing the jacket aside and he is now inexplicably wearing shoes and has somehow lost the diver's knife scabbard attached to his leg. There was no way to have acquired the shoes and lost the scabbard in that instant.
Plot hole: When Angelo sets the Vulcan down in the sea, he blows the canopy and extends the landing gear. As the plane settles, he attempts to release his harness, then has his air line cut by Largo. He futilely beats on the harness release, when all he had to do was pull the face curtain handles to trigger the ejection seat, which would not only blow him clear of the plane, but would separate him from the seat itself. Having trained for two years, for this specific mission, he would undoubtedly be familiar with ejection procedures.
Continuity mistake: When Bond is being chased through the parade, they show the float with the girls on it. In the background behind it as it rolls by is a red sign that says "The Perfume Shop". Later Bond is seen running up to the float and going inside of it to hide. When Fiona runs up to the float and sees the blood on it, the red sign is still visible, which means it was not really moving in the parade at all.