Audio problem: When Bond is involved in a high-speed chase on the way to Miss Taro's house, his wheels are squealing like crazy, but he's on a dirt road. (00:48:10)
Audio problem: When Bond and Honey are on the beach the hoods of Dr No come by boat. On the boat there is a guy shouting through a megaphone. As they sail away again the man waves the megaphone to his comrades and says "full speed ahead". Yet his voice sounds identical to when he was speaking through the megaphone, though he isn't holding it to his mouth anymore. (01:04:00)
Audio problem: When the powerboat shoots at the island, afterward, when the guy with the speakerphone tells them that he would be back later on, he then turns to the driver and tells him to move on, but when he says that, it sounds as though he's still talking in the microphone even thought the microphone is at his side. (01:04:20)
Audio problem: When Bond awakens on the beach and sees Honey Ryder emerging from the water, Honey is singing "Under the Mango Tree", but when she comes out of the water and shakes her head back, her lips are not moving. (01:00:05)
Audio problem: When Bond goes in to see M, you can see Bond speaking just after he sits down. His lips move quite a lot, but there is no sound. (00:10:45)
Audio problem: When the radio controller in London says "Hello, W6N. Report my signals", his lips don't move. (00:05:10)
Audio problem: Pussfeller says "No-one died from my cooking yet" However the audio is overdubbed as it's too clear. (00:30:20)
Audio problem: When we see the band playing in Puss Feller's club it's obvious the man singing is only mouthing the words, the dubbed voice is singing too fast to match up what he's saying into the microphone. (00:30:15)
Audio problem: During the opening credits (while it says: "assistant director") you can briefly hear the next bit of music start 12 seconds too soon - there are a couple of notes from "three blind mice" starting to fade in from the percussion music. But more time was needed, so the last 12 second of the percussion number are repeated. A slightly clumsy edit to cover the credits running longer than planned (best heared with headphones).
Answer: Actually, yes, he would. The key to a vodka martini, Bond's preferred tipple, is that it should be served ice-cold. By shaking the drink, the ice cubes have a better chance to swish around the whole drink than they would if it was only stirred. It apparently also has the effect of dispersing the ingredients better, giving a different taste to the drink. In the spirit of scientific experimentation, some friends and I tried the drink both ways in a blind taste test a while back - it makes a surprising difference.
If you shake it, it turns cloudy.