Dynamic factor models (DFMs) have been successfully used in various applications, and have become increasingly popular. Nevertheless, they suffer from two weaknesses. First, the factors are very difficult to interpret with the usual estimation methods. Secondly, there is recent and mounting evidence that they can be subject to structural instability, potentially leading to an inconsistent estimation of the factors. The central point of this paper is to tackle the uninterpretability issue. We consider two families of methods to get interpretable factors: factor rotations and sparse PCA. When using a large dataset of US macroeconomic and financial variables, they recover the same factor representation, with a simple structure in the loadings offering a clear economic interpretation of the factors, which appears to be stable over time. This provides new lens for the DFM applications, and especially to study the structural instability issue. Using this factor representation, we find no evidence for the emergence of a new factor or for a widespread break in the factor loadings at a given time. The structural instability in the model seems to rather consist in the order of the factors switching over time (apparently in relation with the structural breaks in the data), and breaks in a limited number of loadings which can be localized and interpreted.