What is likely going on is that some of your spatial data have incomplete spatial references. While ArcMap has the capability to "project on the fly", it can only do so effectively if all the data have full spatial references.
For example, you mention that CAD data is being viewed. It is fairly common for CAD files to have a coordinate system that matches the one commonly used for an area, but to lack a projection. Because the coordinates are the same as other data, it loosely lines up with the other data that have the same coodinate system. But because it lacks the projection, it will be off by a bit.
I'd suggest checking the spatial reference information for all your data layers and for ArcMap itself. ArcMap needs to be checked as the Data Frame inherits the spatial information of the first data layer you loaded into it.
ArcMap
Right-click on the "Layers" heading (Data Frame) in the Table of Contents.
Right-click, then choose Properties
Then choose the Coordinates tab and see what spatial reference is set.
For Data layers loaded into ArcMap
Right-click on the layer in the Table of Contents
Choose Properties
Click on the Source tab
Scroll down to see the spatial reference information.
It can be OK for their to be different spatial reference information, as long as the layers have complete spatial reference information. So if you have data in UTM and State Plane, that can be OK.
What are Map Projections?
ArcGIS Help (10.2, 10.2.1, and 10.2.2)
Specifying a Coordinate system
IArcGIS Help (10.2, 10.2.1, and 10.2.2)
Chris Donohue, GISP
