Final answer:
The nurse should monitor the patient's serum creatinine levels to detect potential kidney damage, which is an adverse effect of gentamicin treatment.
Step-by-step explanation:
The nurse monitoring a patient with diabetes who is being treated with IV gentamicin (Garamycin) for bacterial pneumonia should evaluate the patient's serum creatinine. Gentamicin is an aminoglycoside antibiotic that can cause nephrotoxicity (kidney damage) as an adverse effect. Regular monitoring of serum creatinine levels helps to assess kidney function and detect any potential damage early. Blood glucose levels might also be monitored in a diabetic patient, but they are not an adverse effect of gentamicin. Urine osmolality and serum potassium are also less relevant to the specific nephrotoxic effects of gentamicin.