I have created a geodatabase using NAD 1983 UTM Zone 17N. I am placing GCS North American 1983 shapefiles as new feature classes. I appears that although the projection shows NAD 1983 UTM Zone 17N, my map features do not line up - off by about 8 m north/south and 23m east/west. I am new to ArcMap and am having a terrible time getting a plain english explanation of how to correct this. Your help is much appreciated.
I would examine closely the datums that you used and/or had for the source files and the geodatabase. This sounds like a datum difference, albeit small, it is still one (UTM with NAD27 datum versus UTM with NAD83 datum can vary in the hundred'ish range for example)
If the datum is misdefined, then it is doing the adjustment, but it is wrong. if it is indeed a datum issue you should track it down. If it is a data issue then you should look at the spatial Adjustment tools
Make sure both your original data and the data you are adding are defined in the correct projection. If the data was defined as the wrong projection than what it was created in, you can get this error. Bare in mind many different types of projections have the words "NAD 1983" in them because that is the datum name, so it is easy to get confused. One common cause of this I have seen is when the projection really uses the 1927 datum.