The drawbacks of a mixed economy actually 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 dissimilar characteristics. Every of these will share a dissimilar set of drawbacks. A will stifle incomes due to its high tax structure, but will encourage new ideas because of 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 income, but because of 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 may be lowered.