You also have to remember that social mobility can be skewed by wealth distribution. Let's say a person goes from earning $75K to $100K in Canada. That might mean you moved from the 3rd quintile to the 5th quintile. But the same person moving from $75K to $125K in the US might only move from the 3rd quintile to the 4th, even though the US person overall improved their situation more.
http://inequality.stanford.edu/sites/default/files/Pathways-...
The US does not do well on social mobility. Generally, poor families stay poor and rich families stay rich.
Also to be clear, the problem you cite does not exist. This is a percentage relationship between father-son earnings and doesn't have anything to do with quintiles or the magnitude of those earnings.
And after a few google searches, it appears that others have called out the challenges as well[1] and tried to work with other data sets. This analysis found very little different in income mobility between the US and EU and overall...
Canada has the most downward mobility while the U.S. has the least, with Sweden in the middle. We find some differences in upward mobility but these are somewhat smaller in magnitude.
[1]http://www.sciencedirect.com/science/article/pii/S0927537114...
For example if you look for people worth $30million+ per million people, Canada has 186 while the USA has 126. That's about a third more per capita.
And watching the video, you find that 42% of the children of the bottom 20% in the USA wind up in the bottom 20%. Very little of Canada does anything like that poorly.