What were some of the limitations of the New Deal?
It was less a coherent program than a hodge-podge of solutions, some of which worked and some of which didn't. Because it was not coherent, it's been vulnerable to ideological attack over time.
The New Deal wasn't one thing, it was lots of things. Some things didn'r work, like NIRA. NIRA tried to smooth out the business cycle through planning. It was already abandoned by the time it was found unconstitutional. Other things worked great. The Wagner Act moved labor struggles from the streets to the courts, ending a century of nearly constant violence around organizing and strikes. Some things remade the way we live and where we live.
Programs like TVA and REA brought electricity to rural areas that never had them before. Banking reform was another success. So was the home mortgage re-finance program. The agricultural plans didn't really help small farmers who were most hurt by the depression but they did prevent ecological disasters from recurring. Finally employment and infrastructure programs were very successful, employing millions, helping the economy recover, and creating the infrastructure that fueled the success in the war and the postwar boom.
However, this bounty wasn't shared equally. Some New Deal laws were written to exclude industries that were heavily African American and the New Deal continued policies that were discrminatory towards women and African Americans even as some New Dealers tried to expand opportunities for those groups.