During the Choosing Ceremony, each participant is called up to a stage individually. Once there, they must use a knife to cut their hand and then drip a drop of blood into one of five bowls. Each bowl is filled with material that symbolizes one of the factions. There's water for Erudite, stones for Abnegation, glass for Candor, soil for Amity, and coal for Dauntless. While kids are likely to get caught up in the spectacle, adults will notice that nothing about the ceremony is sanitary.
The biggest issue is the knife the participants use to cut their hands. While the scene doesn't focus on it, nothing indicates an individual knife is provided for each participant. Instead, at one point, a man is shown grabbing the knife and wiping the blood from the previous participant off with a cloth before presumably putting it down for the next participant. However, unless that cloth had some powerful chemical on it, there's no way it cleaned the knife to the point that it's sanitary.
Then there's the matter of the bowls themselves. Adults will realize that with all that blood being dripped into them, they should be a gory mess. Yet by the end of the ceremony the bowls look as pristine as they did at the beginning. While that certainly makes the scene easier to watch, it doesn't make sense unless there's some sort of unexplained future technology at work.
