The median is not a true representative of a central tendency in a series where the degree of variablity. So the mean deviation calculated the about the median for a such a series is not completely reliable.
The sum of the deviations from the mean (ignoring the minus signs) is more than the sum of the deviations from median. So, the mean deviation about the mean is not very scientific. Hence, in some cases, mean deviation may not give satisfactory results.
The mean deviation is calculated on the basis of absolute values of the deviations. Hence it cannot be subjected to further algebraic treatment.