Tom Mullen, of Glasgow University law school, advised that the requirement to "endeavour to secure improvement in the quality of school education" was so discretionary that breaching it would be hard to prove in court.
The new duty is weaker than that in the existing 1980 Act, which demands that councils achieve the goal of "adequate and efficient provision of education" and not merely try to do so.
The committee is also unhappy about proposals to abolish the Scottish Joint Negotiating Committee, saying the time-scale was too short and only a limited number of people had been invited to comment on technicalities rather than the principle of abolition.
MSPs still approved the move with only the three SNP representativesindicating their dissent. Nicola Sturgeon, the party's spokesman, said: "It is otherwise a unanimous report but not unanimous support for the Bill as it stands."
The only other note of dissent came from Brian Monteith, the sole Tory, who disagreed with the blessing given to ending the self-governing status of St Mary's primary, Dunblane.
The committee "was struck by the extent and consistency" of concerns by witnesses about relations between HMI and schools and local authorities.
Promising a return to the question, the report stresses the importance of complete confidence in the system.
MSPs want to see flesh on the bones of some parts of the Bill before expressing a verdict. The Executive had not spelled out its national priorities for schools, and so "it is difficult for us to comment in the absence of a set of proposed indicators".
The first debate about the Bill on the floor of the house will be next Wednesday when Sam Galbraith, Children and Education Minister, will be expected to respond to the concerns.