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I've noticed that in Object Mode, if you select an object it will tell you how many triangles are in the mesh. However, is there a way to highlight where they are? From what I can see, everything is made out of quads. It says the same thing for the default cube as well.

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Triangle count refers to the tessellated result of the final mesh, required by graphics cards to draw geometry, not necessarily your mesh polygons.

A four sided face will be made up of two triangles, even though no three sided faces are present in your model.

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To find all three sided faces faces in one mesh, while in Edit Mode select one of the triangles, the use the Select Similar operator Shift + G > Polygon Sides.

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Or If one can't easily be found, do the inverse process, select a quad, then invert selection with Ctrl + i.

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