The HeLa bomb: this really was a bombshell, and there were two issues concerning the cause (contamination, and the incredible vigor of HeLa cells), and one concerning the implications (a whole lot of experiments turned out to be worthless).
Contamination: people were still learning the best ways to grow cells, and they were still discovering all the picky precautions needed to keep contaminants out. Think of it as trying to keep tiny dust motes out of something. You remove some of your sample with a hypodermic needle, and when you pull the needle out a tiny bit of the solution goes into the air as an aerosol. You get a minute drop on your lab coat. It dries, floats off, and lands on your lab bench. You put a clean pipette down on the supposedly clean bench, pick it up, and use it to transfer your cells, not realizing you've added a call. Now people take incredible precautions against contamination, using elaborate sterile hoods--kind of big boxes in which you do your experiments, with air flow systems using filtered air, and a whole bunch of very picky techniques to keep things clean.
The vigor of HeLa cells: these cells grow so much more vigorously than normal cells that a single one can take over a culture, eventually displacing the normal cells. A normal cell landing in your culture might die, but a HeLa cell won't. So contamination is almost certain to occur eventually.
The implications: if you were doing a general experiment, where the kind of cell didn't matter, your experiment would still be good. But if you were trying to find out what liver cells did, and you really had HeLa cells, everything you thought you had learned didn't tell you a thing about liver cells. And if you thought you were seeing normal cells turn cancerous, what you really saw was normal cells being replaced by HeLa cells.
So a whole lot of people weren't working on what they thought they were, and their experiments were no good. Some people lost years of work. I can remember the horror that spread through the biomedical research community when the news broke.