I took classes/exams similar to what he's talking about - they're crap
While I didn't have anything like the clearance Snowden would have had, I did hold a Secret level clearance. After they cleared me, but before I could actually access the data covered by that clearance, I had to "take classes and exams" like he said. Basically you view Powerpoint type presentations that tell you the rules for accessing data, what you can do with it, etc. and then are given multiple choice questions at the end. One could probably get 50% just applying common sense to the exam questions, the rest is just memorization of the right answer to questions that look like they might have multiple valid answers, plus getting down the terminology they use.
I'd say it compares almost exactly with taking the written portion of a US driver's license test, if they used different terms for things like traffic signal, stop sign, etc. The classes/exams I was required to take would guarantee people followed the rules almost exactly as well as passing the written portion of a driver's license exam guarantees you'll follow the rules of the road. Thus, in both cases, effective policing is necessary - and Snowden's claim was that this was not done very well (or) at all. If you think people around you drive poorly now, imagine how they'd drive if they told you the roads were heavily policed but everyone knew there were no cops at all on the road.
When I had my clearance I assumed they were actually monitoring things quite closely, not that I was ever exposed to anything most would consider to be worthy of clearance. My understanding is that that at the "Secret" level they don't protect individually sensitive stuff so much as things that could be sensitive when taken in aggregate or when viewed through a specific lens. Thus, a database showing toilet paper deliveries to military bases around the world might be tagged 'Secret', or possibly even 'Top Secret', because if you became aware of a large increase in the amount being shipped to the base in Riyadh, you might infer some sort of major military offensive in the Middle East was coming.