One of the biggest safety concerns when hiking Longs Peak is altitude sickness. This occurs at high elevation, when you are unable to get enough oxygen. Symptoms include a dull, but throbbing headache, nausea, loss of appetite, feeling dizzy, and vomiting. It is important to take these symptoms seriously; most of the time, they will not get better as you climb, in fact, they will typically get worse. Let your group know right away if you are experiencing any of these symptoms. It is best to turn around as soon as the symptoms arise.
Being physically fit has no bearing on whether or not you will get altitude sickness. The best way to prevent these symptoms is by acclimating your body and lungs, by going on short hikes at lower elevation, working your way up to Longs Peak.
Another safety concern is summit fever. This is not actually a medical condition, as it sounds, but instead a desire to reach the top, no matter what the cost. Weather, late starts, and underestimating the physical challenge all factor in to whether you will reach the summit. If you are doubtful, turn back. Not reaching the summit is not a failure; it is smart to turn back when you need to, and you will still receive incredible views along the way.