Consequences of OWFs for Complexity
This is a late response. 

First, to correct what you wrote: 
Cryptographic pseudorandomness (the one obtained from OWFs) doesn't have enough stretch to derandomize "naturally defined" computational complexity classes. In an old paper (beginning of 80s) Andrew Yao shows some subexponential time derandomization for RP etc using these objects (btw, this is immediate), but no stronger derandomization is known. Note, that in terms of fooling power cryptographic PRGs are stronger than what you need for derandomization but at the same time in terms of their stretch are weaker than their typical complexity-theoretic analogues (this follows by the order of quantification in the definition of the PRGs). 

As Sasho Nikolov mentioned there are plenty of examples in PAC learning. Have a look at a very early paper by Kearns and Valiant on the impossibility of learning formulas and automata (follow in google scholar the references from there). Also, there are consequences in proof complexity through interpolation -- have a look in the also early works by Jan Krajicek and Pavel Pudlak. However, I am not sure if you consider these to be complexity-theoretic implications (but I do). 

-- Periklis