Incomplete multi-view unsupervised feature selection (IMUFS), which aims to identify representative features from unlabeled multi-view data containing missing values, has received growing attention in recent years. Despite their promising performance, existing methods face three key challenges: 1) by focusing solely on the view-missing problem, they are not well-suited to the more prevalent mixed-missing scenario in practice, where some samples lack entire views or only partial features within views; 2) insufficient utilization of consistency and diversity across views limits the effectiveness of feature selection; and 3) the lack of theoretical analysis makes it unclear how feature selection and data imputation interact during the joint learning process. Being aware of these, we propose CLIM-FS, a novel IMUFS method designed to address the mixed-missing problem. Specifically, we integrate the imputation of both missing views and variables into a feature selection model based on nonnegative orthogonal matrix factorization, enabling the joint learning of feature selection and adaptive data imputation. Furthermore, we fully leverage consensus cluster structure and cross-view local geometrical structure to enhance the synergistic learning process. We also provide a theoretical analysis to clarify the underlying collaborative mechanism of CLIM-FS. Experimental results on eight real-world multi-view datasets demonstrate that CLIM-FS outperforms state-of-the-art methods.