What is the effect of the wavelength on the spectrophotometric measurements of protein?
Light absorption happens because of interaction of light with electrons (in a way) such that the energy of the light is transferred to some electrons that moves them to a higher energy state. 

As per quantum chemistry (Bohr's model of hydrogen can be referred for a basic understanding), there are distinct energy states (solutions of the Schrödinger equation) and there are no intermediate levels. Therefore, to excite an electron to a higher energy level the energy of the incident light should match the energy gap between the ground state and the excited state. 

In a molecule, there are different electrons, that reside in different orbitals and environments; only a few electrons can be exited by the energy that UV-Visible range of the electromagnetic spectrum can provide. These electrons are typically referred to as chromophores. You should refer to a book on spectroscopy for more details. A molecule can have multiple chromophores and each may absorb a different wavelength. 

Having said that, there are energy bands (multiple closely spaced energy levels) in the molecule instead of fixed energy state which allows absorption in a range of wavelengths around a value at which the absorption is maximum. The wavelength vs absorption graph will give a peak at the maximum (which usually looks symmetrical but not always necessarily be so).




   From ChemWiki 


The width of this absorption band would differ between different chromophores; so in your hypothetical case, some chromophore which has an absorption maximum at 580nm may absorb 530nm while another chromophore with same maximum, may not.

The Beer-Lambert's law will hold for all wavelengths that can be absorbed i.e. the absorbance would be proportional to the concentration of the molecule (unless there are complex phenomena like energy transfers that may be dependent on concentration; this is unlikely in dilute solutions). 

As a practical suggestion, I would say that if your spectrophotometer has fixed options then choose the wavelength that is closest to the absorption maximum.

If you see the above example graph and let's say your aim is to quantify nitrophenolate in a mixture of nitrophenol and nitophenolate. Then a measurement at 350nm instead of 400nm would give you erroneous result. In other cases a 50nm difference may not matter (for e.g. measuring at 450 for the nitrophenolate). It all depends on what you are analysing. You should know the molecule that you are analysing.