Henrietta’s immortal cells weren’t just important in 
  aiding in finding cures for diseases and the like, 
  they also ended up indirectly causing major reform in 
  how scientists worked with cell cultures, in terms 
  of making sure that samples weren’t contaminated.

This is a huge problem in cell biology, especially when the cell studies you're doing are leading up to human trials.

Once you've got HeLa cells in your cell culture, they're nearly impossible to re-separate. (And HeLa cells are hardier than most, so you can't just kill them.) If you discover that contamination after you've published and sent your cells away for archival, it's really hard to undo that set of mistakes.

In fact, I've tried to order not one, but two cell lines in the past year--based on well-cited publications, mind you--only to get a "contamination letter". (The cell line you want is contaminated. You can still order it, but you'll need to sign this waiver first.)

For a sense of how big this problem is, here are known (often published) examples:

http://en.wikipedia.org/wiki/List_of_contaminated_cell_lines