This is about spectrometry.

How would the presence of salicylic acid affect the results of the spectrophotometric determination of the purity of ASA? Why?

I don't know how you conducted the experiment but I assume you measured a peak in the absorption spectrum of ASA. Since ASA is made from salicylic acid, there would be extra absorbance at the peak you are using. I expect it may shift somewhat, due to the groups added to SA, but, none-the-less, it won't shift enough that there will be no intrerference; therefore, the SA will have you thinking there is more ASA there than is actually there.

Check my thinking.

I take this is uv/visible? The absorbance in the UV/Visible spectrum of ASA is due to the aromatic ring. As this is present in both SA and ASA you will not be able to easily determine the purity of ASA from the UV/visible spectrum.

The better spectrometry way to do this is either infra-red or nmr.