The disadvantages of a mixed economy really depend on how “mixed” it is. For instance, if it is mixed more towards a free-market, there is little regulation (some may see this as a good, though), but if it is mixed more towards a command economy, the control may stifle growth.
Mixed economies can also have different characteristics. Each of these will share a different set of disadvantages. A will stifle profits due to it’s high tax structure, but will encourage new ideas due to its low regulation (this could result in many weird effects such as an economy comprised almost solely of small, well-niche businesses). B will encourage profits, but due to its regulation, some new ideas (and some growth) will be stifled. For instance, if environmental regulations are strict, the building of new plants or refineries might be lowered. This could result in a small number of very large and profitable businesses.