Jo Bauer from the FIA circulates continuously, checking out new parts and procedures, it is frequently the case that it is impossible for him to have seen something before the car first runs.
The problem is that the FIA are not really aware of the most sensitive areas. They are not obvious, either, even to dyed in the wool fans, since many are unintuitive and the teams keep them to themselves.
Weight is crucial, and there was one team in particular who had imaginative ways to cheat this, once the FIA twigged the random weight checks were introduced.
Front ride height is critical for a number of reasons and various ways have been exploited to run the car lower that the flat bottom/plank wear strictly allows. There has been a continuous evolution of ways of limiting what people are allowed to do over the years.
The flex front wing saga was blown out of all proportion, for some reason IMO. It was pretty obvious from wind tunnel tests in 2007 when first looking at the new rules for 2009 that the height of the front wing end plate was going to be a very powerful parameter (and much more so than the 2008 rule). Toyota tested a range of differently flexible front wings, starting at a Bahrain test of the 2009 car in December 2008. The press never got wind of this, mid you, they did not even seem to have realised the 2009 car was there. I am sure plenty of teams experimented with this, but certainly Red Bull were targeted by the press years after the first test of such a thing (and they were certainly exploiting it to the full).
The teams most used to extreme interpretations of the rules are the ones most astute at deflecting criticism IME.