A near-native speaker understands almost 100% of a novel or a paper, listens to a native speaker and understands almost everything, can write with "dignity", recognizes the different "languages" (formal, informal, semi-formal etc.), usually uses good syntax , understands 99% of humor in the foreign language, can follow a phone conversation with a native speaker, is fluent when he speaks etc. From my own experience the most difficult thing to get is a PERFECT PRONUNCIATION .