Cosmology is one of the most interesting and fascinating scientific subjects. It is also one of the most problematic scientific subjects. In fact, cosmology is not a purely scientific discipline noting its intimate relationship with philosophy (and possibly religion) as well as its inherent speculative nature in some of its fundamental aspects due to the lack of real and decisive experimental and observational evidence that can reach (and hence verify and assess) these aspects. In a sense, cosmology is inherently a mix of physics and metaphysics even though its metaphysics is usually treated (in modern cosmology) by scientific tools and methodology and presented through physical concepts and terminology and hence it appears like physics (or it is hidden behind thick layers of physics). In this article we overview the main weaknesses and shortcomings of modern cosmology which suffered in the recent decades (especially in its theoretical sides) from serious problems and challenges due largely to the domination of certain theories, models and assumptions with the absence of a clear and proper epistemological and philosophical framework and lack of regulations that govern the research in this field and determine its routes and destiny. We also propose and discuss briefly some remedies that should be considered to address these weaknesses and shortcomings.