While half of the people nominated to the 200-member body have reported for duty at parliament, the qualifications of one have been questioned and another declined to accept the post.
Lt Gen Thawatchai Samutsakorn was a member and the first party-list candidate of the Chartpattana party in the Feb 2 general election.
But under the 2014 interim charter, an NLA member must not hold a position in a political party or have held such a position for three years before being appointed to the assembly.
Aziz Pithakumpol, the Jularatchamontri, also sent a letter to the National Council for Peace and Order (NCPO) leader on Friday, saying he would not accept the NLA nomination.
The 1997 Act of the Islamic Organisation Administration bans the leader of Thai Muslims from holding a political position but this was not the reason behind his decision.
"He's already the head of Thai Muslims nationwide so it's neither necessary nor appropriate for him to accept any other administrative position or political offer," said sources close to the Jularatchamontri.
It was not the law that prevented him from taking the political position since the 2014 provisional constitution and the NCPO's administrative orders take precedence over other laws, the sources explained.
Despite the presence of a few businesspeople, critics are concerned the lawmaking body will have the mindset of bureaucrats or soldiers.
Commentators on social media networks have also blasted academics and civil society figures who accepted nominations.
While the elected House during the pre-coup period was derided as a "husband-wife assembly", the parliament today is for brothers-in-arms, said some posters on online media.
Thammasat University Council chairman Noranit Sretabutr and rector Somkid Lertpaitoon were also under fire for tainting the anti-military image of the university. Charnvit Kasetsiri, a former rector, also wrote an open letter to call on the pair not to associate with junta-created bodies.
Withayakorn Chiengkul, a famous scholar from the October Generation who is sympathetic to the anti-Yingluck-Thaksin groups, posted on Facebook that Thailand could not copy the Myanmar model of a military-dominated parliament.
"The NCPO is just another political group that seized power while the pro- and anti-Thaksin camps locked horns," said Mr Withayakorn.
The military now controls administrative and budget mechanisms and allots resources as it sees fit, but its agenda and attitudes might not match those of the middle class, said the yellow-shirted intellectual.
Mr Withayakorn urged the people to monitor the work of the NCPO and its appointed bodies. "Thailand has a larger middle class than Myanmar does, so it won't work to have a parliament full of men in uniform," he said.
Wanchai Sonsiri, a former appointed senator from the Group of 40, also said the representation of various groups in the legislative body was not balanced.
The scale is heavily unbalanced as well by gender, with women making up only 12 of the 200 members.
Baramee Chaiyarat, secretary of the Assembly of the Poor, said it was ironic that civil society groups which had supported the ouster of the Yingluck Shinawatra government, and even military intervention, had been shunned by the junta as only three or four representatives made their way into the group of 200.
The NGO nominees to the assembly include Tuang Intachai, a former appointed senator from the Group of 40 and member of a Roi Et educational and health activist group, Wallop Tangkananurak, a child rights advocate, and Monthian Bunthan, who represents disabled activists.
"The NGOs or even academics will become accessories or [decorative] flowers in this parliament, no matter how impressive their speeches are during the meeting sessions," said Mr Baramee.
He also dismissed the hope that more NGOs would be appointed to another body in charge of reform.
"The reform agenda are set by the military and other issues will be shunned. Even the sensible proposals of tax reform on land and buildings and inheritance, I don't think this assembly will pass them. After all, many generals are either the landlords or the landless so they couldn't care less either way," said Mr Baramee.
Ekachai Chainuwat, a Siam University law lecturer, said he would like to ask the NLA members to read the provisional constitution carefully and remember what the coup makers had pledged to society.
"Your primary job, no matter how illegitimately you were nominated, is to build a foundation for a stronger democracy in Thailand. Approving economic projects for the benefits of certain groups should not be your priority," said Mr Ekachai.