<p>I would like to display multiple colors (and potentially shapes and sizes) of data points in a Google Chart scatter chart. Does anyone have an example of how to do so?</p>

You can only use one dataset in a scatter plot, thus only one color.
http://code.google.com/apis/chart/#scatter_plot
From the API description:
Scatter plots use multiple data sets differently than other chart types. You can only show one data set in a scatter plot.