Cat stumbling around. Causes
These are the major causes of a cat stumbling around.

Two cats suffering (or who suffered) from vestibular disease and have head tilt. Vestibular disorder is one cause of a cat stumbling.
Injuries or diseases of the cerebellum. The cerebellum is large and well-developed in felines. It is concerned with a cat’s coordination and balance. Accordingly, if it does not function properly through injury or disease the cat stumbles and has uncoordinated movements.
A blow to the head can cause pressure on the brain. Slight pressure on the brain can result in the cat being stuporous (reduced sensibility). The cat may stumble. The cat breathes normally. The pupils stay constricted (small) when a light is flashed in the cat’s eyes.
A disorder with the inner ear vestibular apparatus (the labyrinth) can cause stumbling. This is because the apparatus maintains the cat’s balance and sense of orientation. It is made up of three semi-circular canals which are sensitive to 3-D movements and gravity. Inflammation of the labyrinth (labyrinthitis) causes the cat to lose balance. The cat may stumble, wobble and fall over. She may walk close to the ground. Her head will usually tilt to one side. She may vomit and have jerky eye movements. Humans suffer from the condition.
The causes of vestibular disorders are, inner ear infection, stroke, brain tumor, knock to the head, brain infection and drug intoxication and thiamin deficiency. As for drugs, aminoglycoside antibiotics are more likely to be the cause.
There may be a congenital defect with the vestibular apparatus. Oriental Shorthairs (and I presume the family of breeds associated with the OSH) are more prone. Siamese kittens with the problem may be deaf. Kittens have a head tilt and circling actions.
Sometimes the cause is unknown – idiopathic vestibular syndrome. In the USA there is an increase in cases of this disease in the northeast in July and August. The cause is probably environmental. It seems, research on this is required.
For idiopathic vestibular syndrome, in most cases, the cat recovers over a period of three weeks with support. A cat may have a permanent head tilt. I saw one such cat at A1 Savannahs in OK, USA.
Injury to peripheral nerves. These are the nerves in the legs and peripheral parts of the body (i.e. outside the spinal cord and brain). A nerve can be torn or stretched. Diabetic cats may have nerve weakness. An automobile accident can cause brachial and radial nerve injury supplying the forelimbs. If the leg is partially paralyzed the cat will stand but stumble.
Photos: Flynn via katsandogz.com. Milo on Flickr, by David DeHetre.