To prevent burns in the bathroom, set your water heater at as low a temperature as possible (120° F. or lower), and always test the bathwater's temperature carefully before plunking your child into the tub. And don't leave him there unattended even for a second. Drowning is a real risk at this age, and so is the chance that your child will try to turn on the hot water, scalding himself in the process.
Falls are another peril for the 2-year-old. Keep furniture, especially beds, safely away from upper-story windows. Window guards are an added safety measure; in some cities, apartment buildings are required by law to have them. All looped window blind cords are a strangulation hazard and should be cut into two strands and secured out of kids' reach.
Poisons remain a hazard now as well. Your child's manual dexterity has increased, and so have her problem-solving abilities, so some heretofore tricky containers are now a snap to open.
To keep medicines (including vitamins) out of reach, put them in a cabinet with a lock on it. Store household cleaners in a high cabinet, safely out of sight and reach. Never transfer a poisonous substance (such as bleach) into a container that looks as though it might hold something to eat or drink (such as an empty milk jug). And remember: Alcoholic beverages can be toxic if ingested by a small child, so lock up all your liquor, too.
Accidents do happen, even when precautions are taken. Keep a bottle of syrup of ipecac (which induces vomiting) in your medicine cabinet, and have the poison control center's phone number handy. Should your child ingest a harmful substance, don't make him vomit unless instructed to do so by a doctor or a poison specialist.