I am always on the lookout for the classic sin of making it look like electromagnetic waves wiggle in space like a snake. I know it's convenient to glue the tangent space to the underlying physical space, but I think it confuses students.
To be clear: the amplitude of the electric and magnetic fields (and hence their components in each direction) oscillate in space/time. Any particular wave though should travel in a straight line (usual caveats apply). Of course you may incidentally also get e.g. sinusoidal variations in intesity perpendicular to the wavevector, but that will be because of the overall beam characteristics.
I don't mean to say I know a better way to show this, and I am aware of many complicating factors. I just think lots of people (my former students and self included) can come away with a wrong idea about how these waves work.