This article investigates the competition for limited attention in a social network with innovation. We consider the case where each piece of information has a fitness as proxy of its quality. The higher is the quality, the higher are the chances of being transmitted. We measure the relationship between the quality of an idea and its likelihood of becoming prevalent at the system level. We find that both information overload and limited attention contribute to a degradation of the system discriminative power. When trust is incorporated into the model and the agents can decide whether or not to accept a meme, we show that both lifetime and popularity distributions have broad power-law tails indicating that only a few memes spread virally through the population reproducing perfectly the broad distributions obtained from empirical data.