Yes, there is no definitive way of making the diagnosis, its more like building a case, there are certain typical features of the persons history and difficulties that mean the starting point is in a good history and then some specialist cognitive testing, Alzheimer's is associated with specific patterns of cognitive difficulties but it may also cause some of the other problems with similar symptoms, so its not straight forward, depression for example is commonly present . Then because some of the symptoms can be caused by other problems a number of tests are carried out to exclude these other causes, many can be identified in simple blood tests. Various scans can be used to exclude some possible causes that can be directly imaged like vascular changes or strokes but in reality they don't add much and the cost can only be justified if the diagnosis is still unclear. Any changes that are identified are often age related and present in those without signs of dementia and many of the changes are only seen at the microscopic level. They do remain an important tool in research. Examination of the CSF is rarely used, its invasive and hard to justify though it may indicate the presence of inflammatory proteins, how significant these may be is debatable.
As Alzheimer's tends to run a lengthy course and is essentially untreatable the diagnosis will become clearer over time, the important thing is to identify and treat anything else that might be causing these symptoms or that might add to the persons problems.