Except that, in this only real close up view of the Hong Kong, we are actually following a body double and Michael Caine, when we get a glimpse of him, is actually being filmed with a back projection. In other words, neither actor was ever in Hong Kong for these scenes and it is likely that a local company was hired to film them or a small unit from the US went out to capture what was necessary for the plot.
Anyway, it's done quite well and luckily for us we do get a brief glimpse of what turns out to be a few streets in the Tsim Sha Tsui area of Kowloon. Here are the grabs.In case you hadn't guessed already, the woman in the green dress and headscarf (conveniently hiding her hair) is supposedly Shirley MacLaine's dancer who Caine wants to recruit for a heist operation. He's following her along Hart Avenue in Tsim Sha Tsui as she walks towards her place of employment.
Luckily for us, this area hasn't changed very much despite the time that has passed (nearly 50 years!) and the fact that a large tract of the area was razed to make way for the U.R.A redevelopment that now has 'The Masterpiece' (and the K11 mall) as its centrepiece.
Anyway, in the first few pictures above we see our body double as she walks south around the rather unique bend of Carnarvon Road where it intersects with Humphrey's, Hart and Pratt Avenues.
As she walks around the corner we see the very distinctive shape of a corner building. This is Rose Mansion and we can also see it in the recent Streetview picture below. This old building on the corner of Prat and Hart Avenues has been around since 1958 and is really about the only recognisable thing left.
After she crosses the road in front of Rose Mansion, our walker heads to the right down Hart Avenue and we get a brief glimpse of how it looked back in the mid-60's (see the last two pictures in the screen grabs). And here it is today. It seems that the right hand side of Hart Avenue is fairly modern compared with the left - and it looks as though the modern buildings have encroached somewhat on what used to be a much wider road.