Measuring tumor heterogeneity
The methods that come immediately to mind are mostly related to next-generation sequencing. You can do deep sequencing on your sample, which is just increasing the coverage as much as possible to find rare events. You can do RNA-seq to look at the transcriptome, ChIP-seq to look at chromatin modifications, and single-cell sequencing (a form of deep sequencing operating on individual cells) to get truly cell-by-cell data, either from the genome (DNA) or transcriptome (RNA).

If you are purely looking at phenotypes, flow cytometry is quite useful for analyzing relative expression levels of proteins, using both extracellular and intracellular markers and stains. FACS is an extension of flow cytometry that allows for the sorting of various cell populations into separate containers. These "purified" samples can then be used in any of the methods listed above.