Let's start with personal safety. Common sense tells us that the higher up that you set the slackline, the higher the distance you can fall. Most people set up their slackline about 1-2feet above the ground. Unless you are an advanced slackliner, stay within your comfort zone. Check the ground under the line for rocks or sharp/slippery objects.
As for those around you, be mindful where you set up the line. If you are in the park, adding colorful hanging markers to the line will make it more visible to children, runners, and bikers. If you set up the line in an enclosed area, make sure not to block the emergency exit. If you choose to set up the line with a lot of tension, make sure to reinforce the ratchet. If the ratchet were to come loose, it would project itself and could hurt you or those around you.
Lastly, we can't forget about the safety of Mother Nature! Many kits include tree protectors, to keep the line from digging into the tree and causing it harm. If your kit doesn't include this, you can use a towel instead. For the safety of yourself, and the trees, scope out the area and choose trees that are healthy and at least ten inches in diameter.