The ad specifically claims there are no ill effects, that they are easy to swallow, and hey, no exercise or dieting required! Ads like this were common in the United States between 1900 and 1920. However, these were the days before the Food and Drug Administration (FDA) so it is not clear is whether the companies advertising tapeworms actually put them in the product. In other words, it could have been false advertising.
Despite the claims, it is not safe to ingest tapeworms, as is detailed in the extensive MedFriendly entry on tapeworms. These worms can grow up to 30-feet in length and can cause various signs and symptoms of illness. If someone ingested tapeworms to lose weight, it could result in weight loss (1 to 2 pounds a week) but this is due to harmful side effects (e.g., diarrhea), interference with digestion due to substances secreted by the tapeworm, and the tapeworm absorbing many of the calories consumed (which is why people could continue to eat what they want). The main problem though is that tapeworm infestation could result in blockage of the intestines and death. A related complication is tapeworm infestation of the brain, known as neurocysticercosis (click link for pictures). Tapeworms can also infest the spine, liver, and eye. They can also cause cysts, malnutrition, and stomach swelling (the latter of which defeats the purpose of weight loss). Of note, pork tapeworms are even more dangerous than beef tapeworms.
Many people reading this who are pet owners are already aware of the dangers of tapeworms because you try to keep them away from your pets. Tapeworm infestation in pets and humans is treated with specific medications designed to kill the worms. In people who use tapeworms for weight loss, once the tapeworm is killed the weight returns because no lifestyle changes have taken place. There is no guarantee, incidentally, that the tapeworms will easily be destroyed with medication.
Contrary to some rumors, famous opera singer Mary Callas did not lose 80-pounds from tapeworms or die from tapeworm dieting. In fact, she attributed her weight loss to a regular diet of salad and chicken. While Callas had been afflicted with tapeworms, this was because she sometimes ate raw meat, which is prone to tapeworm contamination.
These days, it is illegal to import or sell tapeworms in the U.S. and the FDA has banned tapeworms for dietary purposes due to the dangers the pose. There are places in Mexico where people can pay about $1200 to $1500 to infest themselves with beef tapeworms, supposedly identified microscopically.