I started riding in the late 60's but only rode middleweight bikes up till the late 70's so I don't remember the 'high speed weave'. But I do remember the 'low speed wobble' and I always cured it by replacing the front tyre with better quality rubber, usually Michelin.
The other point that comes to mind is that, at the time of this film, the motorcycle manufacturers were only just starting to come to grips with the power output of these new big bikes and frame & suspension technology hadn't caught-up yet. I can vividly remember Ross King on the Kawasaki 500 H1 Mach111 violently wobbling up the hill at Amaroo Park at the Castrol 6-Hour Production race and eventually hitting the rock wall on the outside of the bend and being severely injured. In those days the front forks had no real bracing other than the flimsy front mudguard and I noticed in the film that the forks were moving independently. When I got my first 'big' bike, a Yamaha XS1100G, one of the first mods I made was to fit a clamp-on fork brace to improve the rigidity of the front-end.
Another interesting bit was the effect of rider weight and body position. I've always been on the beefy side, so maybe that's why I never experienced the 'high speed weave', but if I had I doubt I would have thought to lie flat on the tank to resolve the situation.