How can I record the cognitive state of my father with dementia?

You could try. Journaling your observations of him.
Dementia. Memory, orientation, self care, alertness, attention, changes at night such as confusion or sleep patterns.
Dementia records. I can suggest a couple of ways. (1) ask him to draw a clock showing 3 o'clock. Alzheimer's patients lose their spatial sense early in the disease and cannot do this correctly. If you do it every few months you will likely see a progressive deterioration. The other issue to track is his competency. See my recent blog at: http://drlifestylesevidenceforhealth.Blogspot.Com/2012_02_01_archive.Html.