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.