Your construction contract should have some language on warranty and the term and conditions. Also check with your State office of the Attorney General or the Contractors License Board as to any required warranties that the builder must provide by State law. There may be other warranties expressed or implied that may be required pursuant to State and common law. Even if there is no language in your contract stating such, there may be warranties that must be honored. In addition there are various manufacturers and building material warranties provided through your builder but given directly by the respective manufacturers such as appliances, roofing, siding, windows etc.Be sure to get all the warranty documents from your builder. There is also a Federal law called the Magnuson-Moss Warranty Act that protects the consumer against faulty building products. You should have completed a punchlist with your builder during a final walk-through and acceptance inspection. If you did, then the builder must fix the items that he is responsible for. If a punchlist was not completed, you need to do this right away. Even if you missed a few things that may appear later (that the builder is responsible for within the warranty period), you are still within your rights to have the builder do the corrective work.
Consult a real estate lawyer experienced in "construction defect" cases to get the specific rules for your state and contract.