Why don't first-world universities use video surveillance to catch in-class cheating?
This is one of those problems which may seem like they can be relatively easily alleviated, but in practice they face many challenges.

For example:


properly videotaping and audiotaping a classroom would require the careful placement of many cameras and microphones; you also have to consider the testing and maintenance of all the equipment
signal processing is not yet at the level where it can catch all the inventive ways students cheat, so your system would still need substantial human involvement 
many legal/ethical/moral considerations
students will always find ways to circumvent anti-cheating systems


Given that typically only a small percent of students cheat and that examinations are held just a few times a year, it seems unreasonable to sink so much time, money, and effort to catch some, not even all, of the cheaters.

Also, there are many easy "tricks" which can be used to discourage cheating, e.g.


make exams challenging enough so that students don't actually have time to cheat
include problems which require working out and which cannot be readily copied (or whatever)


But most importantly, instead of trying to catch cheaters, it's much better to actively try to educate your students why cheating is never a good idea and why cheaters only cheat themselves.