Final answer:
Visual impairment is the condition that could lead to difficulty in self-administration of insulin therapy in a diabetic patient, due to potential issues with accurately measuring and delivering insulin doses.
Step-by-step explanation:
A nurse reviewing the health history of a client who has diabetes mellitus and is starting insulin therapy should identify which factor that might cause difficulty in safely self-administering insulin. Among the options provided, visual impairment is the condition that is most likely to cause difficulty with self-administration of insulin. Although conditions like asthma and hypertension have their challenges, they do not directly affect a person's ability to see and accurately measure insulin doses. Conversely, arthritis may affect the manual dexterity required for insulin administration but does not necessarily impair the ability to visually measure the dose. Visual impairment, however, could directly hinder the client's ability to accurately draw up and administer the correct amount of insulin, thereby posing a significant risk for errors in dosage.