Nearby Breeding Grounds
Because pests usually hide, it's likely that you won't see one on your initial tour -- even if an infestation is present. But you'll do well to identify some likely breeding grounds for pests in and around the property. This will give a clue as to whether the place is already infested or if it has a high potential for future infestations.
Mosquitoes, for instance, breed in stagnant water. Pools of stagnant water around the property suggest that mosquitoes could be a problem in the summer (something to keep in mind when looking at a property in the winter). If you rent a house where there's a pond, ask the landlord for a circulating pump, or consider purchasing one yourself.
If the apartment building is adjacent to an unkempt alley with garbage from adjacent establishments, this is a bad sign. And because both mice and rats love wires, look for electrical wires hanging in unenclosed areas. Check around gas and water pipes, which are also favorite hangouts for rodents.