Common problems people have when descending in water include issues arising with their BCD inflator hose, and utilising the whole BCD in terms of buoyancy displacement.
Problems descending with full lungs
One common scenario you see is people sitting at the surface trying to descend, a lot of the time they're a bit nervous or excited, and so they're dumping all the air out of the BCD, but they're holding their breath and they forget that their lungs are the BCD itself. A very important thing to remember is when you are full of air and you don't exhale enough, you're just going to stay at the surface or have trouble getting down. You might get a little below the surface, but you're not going to be able to descend effectively. You need to exhale. You'll find yourself slowly descending from there.
Body positioning in the water
If you think about how the bladder on a BCD is designed, it is in a sort of a horseshoe shape. Air is going to get trapped in certain pockets based on how you're angled in the water. If you're trying to dump air from one side, but all the air is stuck in one corner, that's not going to do anything. A really simple fix to that is just to lean the other way. It's going to push all the air out and you can dump it from there.
Another thing to keep in mind is how your body is positioned in the water. If you're 5 or 10 meters below the surface or even deeper, you might be flat and start to float up. If you're having trouble dumping the air, you can always lean forward, reach back and pull your kidney dump. Air will escape from there.
Another common issue you may face is if you go to one side and you're lying flat your inflator hose may bend, which will prevent the air from going up and down. It will just get trapped. All you need to do is come back vertically, pop your hips forward and press the inflator hose button. The air will escape from there.
These scenarios are just some of the common problems and solutions divers encounter and often overlook because of panic. Usually these issues are simple to solve.