Babywearing has been practised across the world since centuries ago in many different ways, it is extremely safe.
The most important thing to consider when looking at safety in slings is you child's airways - is there room to breath? There should be absolutely no fabric covering your child's face at all. This includes sleeping hoods and hats - make sure they cover the head if needed, but not the face. Also - consider your child's position - is their chin on their chest? If so, they could find it difficult to breathe, so its recommended that you change positions immediately. For this reason I don't recommend horizontal cradle positions, instead an upright position is preferred. If carrying your child on your front, their head should be positioned somewhere between your breasts and your chin. If you don't have breasts, then somewhere below your chin is fine. That way you can see where you are going! If you are carrying your child on your back, ensure you are able to monitor their breathing by feeling their breathe on your neck or being able to see them by glancing over your shoulder.
Essentially there are two ways to make sure your child stays safely in a baby sling or baby carrier - ensuring that they have adequate support below them with no room to slip through and making sure than their back support is high enough that they are unable to lean too far and flop out.
Finally, be aware of external hazards such as tripping over things or bumping into things beside or above you. Remember, tripping or falling with your child in a carrier is likely to result in a better outcome for you and your child than if you were carrying them in your arms as you often have hands free to protect your child and or break your fall.