Does the curve go near your data points? In rare cases, the curve may be far from the data points. This may happen, for example, if you picked the wrong equation. Look at the graph to make sure this didn't happen.
Are the best-fit values of the parameters scientifically sensible? Nonlinear regression programs have no common sense and don't know the context of your experiment. The curve fitting procedure can sometimes yield results that make no scientific sense. For example with noisy or incomplete data, nonlinear regression can report a best-fit rate constant that is negative, a best-fit fraction that is greater than 1.0, or a best-fit Kd value that is negative. All these results are scientifically meaningless. Also check whether the best-fit values of the variables make sense in light of the range of the data. The results make no sense if the top plateau of a sigmoid curve is far larger than the highest data point, or an EC50 is not within the range of your X values.If the results make no scientific sense, they are unacceptable, even if the curve comes close to the points and R2 is close to 1.0.
If the answer to all three questions is yes, then it makes sense to delve into the numerical results of nonlinear regression in detail.