Limited research efforts have been made for Mobile CrowdSensing (MCS) to address quality of the recruited crowd, i.e., quality of services/data each individual mobile user and the whole crowd are potentially capable of providing, which is the main focus of the paper. Moreover, to improve flexibility and effectiveness, we consider fine-grained MCS, in which each sensing task is divided into multiple subtasks and a mobile user may make contributions to multiple subtasks. In this paper, we first introduce mathematical models for characterizing the quality of a recruited crowd for different sensing applications. Based on these models, we present a novel auction formulation for quality-aware and fine-grained MCS, which minimizes the expected expenditure subject to the quality requirement of each subtask. Then we discuss how to achieve the optimal expected expenditure, and present a practical incentive mechanism to solve the auction problem, which is shown to have the desirable properties of truthfulness, individual rationality and computational efficiency. We conducted trace-driven simulation using the mobility dataset of San Francisco taxies. Extensive simulation results show the proposed incentive mechanism achieves noticeable expenditure savings compared to two well-designed baseline methods, and moreover, it produces close-to-optimal solutions.