Not exhaustive: The list of fundamental duties is not exhaustive i.e. it doesn’t contain other important duties like casting vote, paying taxes, etc.
Meaning: Some of the duties mentioned are ambiguous & difficult to understand for the common man like the "composite culture" mentioned in the Fundamental Duties.
Non-justifiable: It can’t be questioned in the court of law for enforcement. So, it is of no use even if it is included in the constitution. But still various other acts have been formulated by the government which gives effect to these Fundamental Duties & help to punish if not practiced.
Unnecessary: Some critics argue that these duties are so general that they will be performed by any citizen of India. There was no need for them to be added in the constitution.
Place in the constitution: It has been added in the Part IVA i.e. after Part IV (Which belongs to the Directive Principles of State Policy which are nonenforceable even with the court of law). It has given the Fundamental Duties a nature of non-obligation. Instead it should have been placed as the Part IIIA i.e. after Part III (it belongs to the Fundamental Rights). It should have been given power at par with Fundamental Rights.