Heater – check if there is any weird smell or responsiveness. Is it central heating, or just a wall unit? The majority of the time heat and hot water is included in the rent, but make sure of this!
Windows – do they let in any noise? For renters who have pets: are there screens? It would be a smart idea to check for breezes, too. Do all windows lock (or at least those that can be reached from the outside)? Sometimes, there are slow leaks of air from the outside, which require you to unnecessarily turn up the heat.
Water – turn on all of the taps, and check how hot the water gets, how long it takes to get hot, and shower pressure. Do sinks back up? Sit by the sink for at least a minute or two to fully test this out. Believe it or not, this will have a huge impact on your apartment experience.
Potential weekend-wakers: church(es) nearby, early gardeners outside, children, garage door under unit, streetcar/bus line, construction. One of the main reasons why I moved out of my last apartment was because of the obnoxious construction outside my building.
What happens if there is a fire emergency? Is there a clear escape? Locate fire alarms and look for extinguishers in common areas. Check for a carbon monoxide detector and if it’s provided/required.
Is there noise from above/below/next door?
Are pets allowed? Are common areas carpeted? (Could harbor fleas.) How many other pets are in the building? [Does your next-door neighbor run a dog-watching business in their unit? Learned this one the hard way.]
Can bikes be securely stored? Do they have to be kept in the unit? You may want to buy a bike for Spring classes (just in case you feel like biking to Central Park on a sunny day).
What subways are close by? Can you walk to school or work?
How does the bathroom look? Does it have a fan/window/circulation? Check for mold and discoloration in the bathtub.
Where are the restaurants, bars, clubs, coffee shops?
Readers: do you have any other tips for other things to keep in mind?