My cat whines occasionally some nights, and although annoying, I'm actually concerned that something might be hurting him. Are there any common cat problems that cause them to whine at night?
Cats are considered to be crepuscular and/or nocturnal creatures. The exact nature depends on the cat itself. In either case, they are generally more active at night, and less active during day which is why cats end up sleeping for most of the day. At night, they are more awake and can become restless since the whole house is sleeping. This is the most likely cause for cats whining/meowing at night.
They can also whine for a variety of other reasons, if they are bored, disoriented, curious, hungry, and sometimes sickness causes them to whine as well. I don't think you are hurting your cat as you phrased it, it's just natural for cats. You will probably have to do some detective work to narrow down the cause if there is one particular reason that it is happening.
Personally, my cat sleeps very well at night when I leave a nightlight turned on in the hallway. Generally we use the nightlight for ourselves (if we have to walk in the house at night but don't want to turn on actual lights), but this seems to have a calming effect on my cat. Perhaps this would solve your problem.