You are correct that children learning language are constantly failing in some manner. There has been a lot of study of the language acquisition of children. However, the way in which children fail and do not fail is specific. Some things children will fail at a number of times until they learn. On the other hand some rules of grammar, logical principles and parameters children seem to pick up immediately, and in Chomsky's view are even innate.
So you can divide theoretically possible failures into two categories - ones theoretically possible that are not made, and ones that are theoretically possible and are made. The first category is what he is talking about.
Also - there are different languages with different rules, and people learning a language have to learn the rules of English which are different from Spanish which are different than Japanese. Although in Chomsky's view, these languages are all so similar (compared to say the recursively enumerable language a Turing machine uses), they are virtually identical from a theoretical point of view.
Also - children make grammar errors such as first saying "I go to the store" (correct) and then "I goed to the store" (incorrect). These errors were not made by data they acquired! The errors children make are showing they are beginning to understand grammar rules, it's a sign they are going off a series of rules and not just regurgitating data they have acquired.