I am not from Amsterdam but I have family there, so I am there fairly often, perhaps I can help.
Your question depends on your definition of 'quasi-legal'. Cannabis is *not* legal in Holland. However, they have made a decision not to prosecute small time offenders. This means, a blind eye is turned to possession when the amount is very low (personal use amounts). They also grant licenses to owners of 'coffee-shops' to sell cannabis with some fairly tight regulations. I believe the idea behind this is that, as has been discovered in basically every other country on earth, people want to smoke a joint from time to time, and it is better they get it from a regulated (and more importantly, taxed!) business, rather than some guy on the street who will almost certainly try to push the more addictive stuff on to the customer for higher (tax free!) profits.
However, what is not tolerated, is massive scale, cannabis farming which is then sold on for huge profits (without tax being paid, are you spotting a theme here??).
The Dutch are an eminently sensible race. Probably my favourite bunch of people. They are smart, direct (this comes across as rude at first, but once you get used to it, it's quite charming!), and very business minded. They actually are quite liberal, but they are also completely aware of how much extra gold goes in the coffers from all those tourists who you will see sparked out on a public bench at 10AM.
People will smoke weed, people will pay for sex, it simply cannot be prevented in any society that has the slightest freedom (or isn't batshit crazy religious!). The dutch say.... ok, get on with it, pay your taxes and don't make a nuisance of yourself and you are fine by us! I reiterate... eminently sensible!