From the scale on the negative end the peak height appears about around 0.4 OD, which is more than enough to get a good, noise-free spectrum (in fact, you shouldn't be too much higher than this - usually around 0.1 OD is a good range). Moreover the shape of the peak looks strange to me. What is this sample?
I suggest running a sample that has a clear and strong absorption peak with a well known extinction coefficient and peak maximum. Do you have any commercial dyes or pigments in your lab? If not, you can buy something pretty cheap to validate the instrument. Also run a blank (solvent only) to make sure the baseline is good (flat).
UV-Vis instruments are pretty low maintenance but lamps do eventually die. If your lamp is near the end of its life, it may not be putting out enough light, which could cause a noisy spectrum even for a strong absorber. Alternatively, if your sample has any turbidity to it, this can also cause noise. This is why I recommend using a standard and a blank to see what those spectra look like - this will help you diagnose whether it is your sample or your instrument.