The short answer is “it depends.”
Let me explain.
There are some instructions that the judge gives to the jury at the end of the case that if mistaken, might be considered inconsequential regardless of the jury outcome. That is known as a “Harmless error.”
On the other hand, there are specific judicial instructions that if given incorrectly, could have disastrous results for the litigants. It could mean that the jury renders a verdict against one side or the other based upon the incorrect law that is provided to them.
At the end of a trial, the judge is required to give the jury the law as it applies to that case in New York. The jury is then given a series of questions they must answer.The jury is told that they are the triers of fact. They must determine what actually happened. Then they must take the law as it is given to them and answer questions about whether there is liability or wrongdoing, whether the wrongdoing caused injury and whether the injury is significant and/or permanent.
Obviously, no judge wants to give the jury the wrong instructions. However, many times the instruction that is provided to the jury is often hotly contested by both sides. Each attorney wants the most favorable jury instruction given. The judge ultimately makes a decision about which of the competing instructions are to be given depending upon the facts of the case and the type of case.
If one side loses, they will always look back at the judge's instructions to the jury to see whether he gave the proper jury instructions. On appeal, the higher court will review issues of law that may not have been transmitted correctly to the jury. If the higher court determines that the judge's instructions were not appropriate, they have the ability to throw out the verdict and to order all the litigants to start a new trial over again.
If the appellate court determines that the judge's instructions constituted harmless error, they likely will not touch the verdict.