Does it have a view and sunlight or is it blocked by other buildings or is it facing the wrong way from the sun?

Checking whether there any pending resource consents that will probably affect the apartment block in future, for example, plans to build a high-rise hotel next door?

Is there a balcony so that the owner can enjoy the view or afternoon sunshine?

Are there any other facilities in the complex, like a gym and swimming pool?

Probable enquiries about your neighbors to find out if noise could be a problem.

Are the near-by apartments rented? If so, do the renters constantly change as these types of neighbors could pose a problem later.