During the fight scene at the boarding house, a little table with flowers on it was tipped over, and a second later was standing upright, waiting to be thrown by the bad guy at Simon.
When Simon is reeling in the marlin, he is sitting on the right side of the boat and the reel is on the bottom of the rod. There is one close-up shot of the reel and part of Simon's lap and the reel is on top of the rod and you can see the side of the boat on Simon's right (he's facing backwards) which means he is now sitting on the left side of the boat. When the scene switches back to a long shot, Simon is again on the right side and reel is back on the bottom of the rod.
During the fishing boat scene, all of the boat's dash gauges read "zero" even though the engine sound could be heard and the boat appeared to be in motion. About 9 minutes in.
Around 3 minutes in it is clear the background is edited in. 20 seconds later they go to close-up of Simon (Roger Moore) and the 'distant' background casts shading shadows on his cheek. Then they switch to the boat captain to whom he is speaking and the background projection is showing on the fishing pole he is holding.
All of the the views from the stern of the fishing boat show the same footage with the same distant object in view.
Simon doesn't know what a daiquiri is, despite the frozen cocktail being popular in the 1960s and the fact that he regularly drank Manhattans (a more complicated cocktail) and in one episode gave a clueless waiter instructions on how to mix a rumhattan.
Most scenes from the water that show land in the background are not Miami Beach. There are hills (such as the water-ski scene) and the beach is narrow and sloped.