What are the short comings of …

The Wurtz reaction is limited to the synthesis of symmetric alkanes. If two dissimilar alkyl halides are taken as reactants, then the product is a mixture of alkanes that is, often, difficult to separate as the difference in boiling point would be very low in these cases therefore distillation wouldn't work.

Also, since the reaction involves free radical species, a side reaction occurs to produce an alkene. This side-reaction becomes more significant when the alkyl halides are bulky at the halogen-attached carbon. This is because the activation energy required becomes significantly high, so the alternate elimination mechanism is favoured. That's why you should only use primary alkyl halides for the reaction. otherwise use a reagent in which the tertiary or secondary carbon is attached with sodium metal.