Physical Danger
You are handling needles, taking blood from people, some who have infectious, deadly diseases. This is not a danger-free job.
You will have to get regular tests for infectious, blood transmitted diseases and take every precaution to protect yourself from getting stuck with the needles you wield.
Gloves are essential and must be checked and worn at all times.
Waste must be disposed in the hazardous receptacle designed for your used needles. Note, any time you see red warning signs and the big skull and cross bone sticker, realize there is a possible danger and be super careful.
You will also be around sick people a lot, so if you don't have a particularly strong immune system, this might not be the best choice of profession.
You also run the risk of getting kicked, punched, or hit by people who absolutely freak out at having their blood taken. While it's not often you have to worry about getting punched in the face, you really need to be prepared for anything when dealing with the general public. You could be working in a hospital and be asked to take blood from a violent psychiatric patient. Make sure you follow all protocols and be safe.
On the upside, you'll be working in a climate controlled lab with others around you, not slaving away in a coal mine.