Little known fact is that this is the first time Sean Connery actually appears as James Bond during the iconic gun barrel opening. Due to unexpected complications in shooting the sequence (mostly due to the camera being unable to focus on both the barrel details and whatever was on the other end simultaneously) a stunt man portrayed Bond largely in silhouette for the intro in 'Dr. No,' which was then re-used for 'From Russia With Love' and 'Goldfinger'. It was only when new camera technology became available that the scene could finally be re-shot in proper definition for this film, with the proper actor playing Bond.
When Bond plus guard fall into the pool and have the shutters close over them Largo gets the gate opened to allow sharks into the pool. When they were shooting this, there was supposed to be a sheet of glass in the water with the sharks on one side, and Sean on the other. Unfortunately, a couple of the sharks got round it and when Sean opens the door to go through to the other pool, he's nose to nose. At this point he's not acting. Watch his face for the genuine look of horror.
For a very long time, the working title of "Thunderball" was "Mister Kiss Kiss Bang Bang". Indeed, the change of title was so late in the production, that composer John Barry was asked to write a title song called "Mister Kiss Kiss Bang Bang". You can hear the 'alternative' title song in the DVD Special Features section
The method used in the end of the movie to pick up Bond and Domino from the life raft is called "sky-hooking". When the retrieved object is picked up, a winch reels it in, line and all (this is not featured in the final shot). It is now barely used, if ever, since helicopters nowadays perform the same job safer and more precisely.