When making a calibration curve, do we have to use the wavelength at maximum absorbance? If you are making a calibration curve for $\ce{CuSO4}$ where you plot absorbance against concentration, does the wavelength have to be exactly at the maximum of the peak? Or can it be somewhere else along the curve of the peak as long as it is consistent among all the measurements and still get an accurate result?
No it doesn’t. Measurements can in principle be made at any wavelength.

If there are two colored specimens in the same solution, it is actually better to measure at the wavelength where the difference between the spectra is as high as possible.

Measuring at a peak has some advantages: the absorbance is high, giving a good signal/noise ratio, and if the wavelength varies a little it has less effect on the absorbance when measured at a peak than at a slope of the curve.