Crime novels to the contrary, it is hard to dispatch someone with a needle unless you are expertly trying.
It is standard practice to make sure air is cleared from a syringe before pushing the plunger, but the chances of death occurring because of the air a fine needle might carry in a normal injection into muscle or skin are rather low; a small bubble would normally be dispersed in the tissue.
A bubble of air in the circulatory system, called an air embolism, can potentially be fatal, but usually only if the air is introduced into a fairly large vessel.
If an arterial bubble cuts off oxygenated blood going to the heart muscle or a key part of the brain, for example, it could cause a heart attack or stroke. An air embolism in a large vein can also cause a dangerous air lock in the heart.
The main risk, however, lies in procedures like intravenous drips or in surgery. The rule in open heart surgery is “no air, anywhere,” and heart-lung machines have filters for bubbles.
There are also detectors for intravenous procedures.