An interesting study (Michael D. Lee and Rachel E. Reilly, 2003, "An Empirical Evaluation of Chernoff Faces, Star Glyphs, and Spatial Visualizations for Binary Data"), "found that both glyph visualizations lead to slow, inaccurate answers being given with low confidence".

I think Chernoff faces are the pie charts of multidimensional visualization. One of the problems with both designs is the familiar metaphor. We shouldn't try too hard to translate abstract data into some identifiable images. Not only there are cognitive/perceptual issues to be solve but also you can't just remove your social stereotypes from the analysis of something as powerful as a face.

For continuous data you always have things like scatter plot matrices, but you must be sure that your audience understands them...