Mice are excellent models for many diseases but not all. When possible we study cell culture, then mice, then humans and there are rigorous ethics committees that require justification for the study, we don't just do these studies for no reason. Their metabolism and physiology is pretty similar to ours, which makes them useful to study inflammation, cancer, diabetes and other malignant/metabolic/genetic disorders. They have a 21 day gestation period and research mice are essentially all clones which eliminates genetic variability as a factor (making them excellent for reproducibility in a timely manner)

some drawbacks include the spine, they're haunched which makes it difficult to study something like scoliosis, we do this in zebrafish actually. Also I believe they have some mild immunological differences like ratio of circulating white cells and bone marrow differentials and minor differences in some proteins. Basically anyone doing these studies has years of training and really knows what they are doing, they would not be allowed to conduct them unless it was absolutely necessary to answer a specific question. Mouse work is a lot more complicated/interesting than this but I think I've made my point for now.

Source: wrote a portion of my thesis on justification of using an animal model for obesity research, then an 8 year career in a pathology core/phenotyping lab.