From my understanding they can have a couple of behavioural problems, first one being some like to chew everything in sight (as I said some, not all), however you can manage this by making sure they have toys they like whilst outside the cage, amongst other ideas some of the more experienced members can suggest. They get easily bored if they don't have enough stimuli, again lots of toys and variety, as they love to play. You will find they will be extra noisy if they are bored. Finally they can be a bit bitey. Sometimes they may just give an odd bite for no reason, but most of the time its due to hormones, pin feathers, or various other issues.
All of the above are possible problems that not every Conure will have and as long as you are willing to put in the time, effort and research they can all be overcome, or at least managed. I hope that helps. They are such a lovely species and fantastic companions.