While watching the hunting scene down from the hotel on skis in "On Her Majesty's Secret Service" I was wondering why (and if) they are going quite slow. If I had the same hill while on skis (and being hunted) I would have chosen a much straighter line down the hill, resulting in a higher speed. Is it just an impression one gets from the movie that the speed of the skiers is quite slow, and they are going really fast? Or are they also slow in reality, and it is because of something else? Furthermore, the accident Bond has (where he loses one of his skis) looks quite bad, i.e. I would have expected him to damage at least one knee. Is that exaggerated, or is it just luck?
As someone who skis 50+ days a year let me try and address some the of the questions you pose. For reference I went and reviewed the scene you were talking about agin(it's been a little while).
A couple of caveats before I begin regarding the equipment being used in this scene. The filmmakers give us a real good look at the skis and boots James Bond uses at the beginning of this scene. The brands (Bond often used Olin skis) aren't important but the technology is. The skis in this scene look to be from 200cm to 220cm (taller than Bond) in length and probably not much more than 60 mm under foot. His boots aren't leather but the shell appears to be a softer material and uses a lacing system. So what does all of this mean?
You really can't compare what you see modern extreme skiers doing today with the stuntmen in this movie. Modern skiers use much wider and usually shorter skis that have various types of camber that make them an order of magnitude easier to ski. They just are WAY more stable and will chew up crud, powder, bumps, or anything else you throw at them. Modern boots are much more stiffer and allow the skier to drive the ski as hard as they want. The skis Bond and the bad guys use in this scene aren't even close. This is one reason why so many people switched to snowboards in the late 80' early 90's.
So with that said, let's address your questions.
Why...are they going...slow? I am assuming you aren't talking about the blue/green screen portions of this scene. At about 30-45 seconds in the camera looks up at Bond coming down at the top of a section with quite a few moguls and he makes what appears to be quite a few turns. A few seconds later the bad guys take off after him and we see the same camera angle from below the skiers.
The problem with looking up on a steep slope is that it never, ever looks that steep. It's really an optical illusion. Moguls are typically steeper on the side you approach them and then fall off. This is because most skiers are checking their speed as they approach the mogul which then builds up over time to become more and more difficult. The reason the skiers at this point of the scene aren't just charging straight down the mountain is that the hill is much steeper than it looks and they must control their speed through the mogul section. Now there are guys and girls out there who can just eat up the whole section without stopping but the clean Stein Eriksen old school turns that these stunt men use looks great on film.
At about 1:30 to 1:45 in the scene the skiers make a series of pretty good sized jumps in and out of the ridge line they are skiing. If you have ever skied in Canada or the Alps, even with a guide you are never quite sure what is in front of you. This scene is clearly off-piste. That means you can be charging across a seemingly innoculous section and 1 second later there is a cliff in front of you. If I am being chased by bad guys with machine guns in this terrain or the one doing the chasing, I'm gonna be a tad cautious. In spite of this, these stunt men make some pretty nice jumps.
Finally, just before Bond loses his ski the terrain begins to involve more trees. Tree skiing is a blast but tress always win. Enough said.
Was...Bonds accident real? At about 2:30 into the scene, Bond loses a ski and then takes off on only one ski. The accident looks bad but is actually quite harmless and is an example of an experienced skier who knows 'how to fall'. The ski actually comes off well before he hits the snow bank. Anyone who has skied has surely 'caught an edge' before. This is what happened to Bond. Catching an edge can take many forms but it basically means you got one or more of your feet tangled up. The bindings in this scene were probably set a little loose so that the ski would release fairly easy. After the ski popped off Bond actually slides over on his side and then slides up the snow bank. Watch all of this in real time and it looks he slams his knee into the snow bank and his ski pops off. Another example of how fast the stunt man was really going.
It should also be noted that the 1 ski, sequence is very real. I am pretty sure CGI was not available in 1969. The ski double for Bond, Vic Armstrong, should be given special props. Legit.
After breaking this scene down and then going back and watching from start to finish without stopping I think the green/blue screen parts with the few flat areas they sprinkled in (where the skiers are pushing and skating) are the main culprits for the scene appearing to be slow. Wikipedia mentions that some fast motion editing was also used, which can give a 'fake' appearance to anything. In my opinion, during the real ski sequences, these guys were skiing fast and well.