There are many scenarios that solve your problem. Here are a few. They aren't at all mutually exclusive and probably all would work together.
Your Society is a Giant Mexican Standoff
If everyone knows magic, then how can anyone do anything bad with it without immediately being jumped by his/her peers? Literally every man, woman and child is a walking weapon of mass destruction in your society. The only way anyone can stir up trouble like that is to be orders of magnitude more powerful or to work in a group.
As others have stated, we have the entirety of chemical knowledge at our hands in our modern society. This is akin to your magic. Anyone can make nerve gas and explosives very easily and do lots of damage with chemicals that are easily available. Oklahoma city is a perfect example of this. The only thing stopping us all from making nerve gas explosives is a tacit social understanding that it is not acceptable and a misunderstanding that it is difficult.
Even so, common chemistry knowledge is abused "See: Meth Lab," but even then people are careful about it since they don't want to go to jail.
In your society, bad behavior is presumably punished, so it's going to be rare that someone will abuse magic to a massive degree.
The state police of your magical world are likely to be the most well-trained in magical combat, and as such should be able to do a relatively good job of keeping the peace.
Big Spells Should Be Difficult
You mention blowing up a continent. How plausible is it that a single person would be able to cast such a powerful spell? Nearly all magic systems require the use of mana or some other personal energy, and the energy required to cause mass destruction is almost certainly going to be proportionately massive. Such a powerful spell would likely not be something that could be easily cast, and would almost certainly not go under the radar.
Your state's magical police would likely catch wind of such a plot and attempt to disrupt it. For smaller scale destruction, you have the same problem we have with terrorists today: namely that it is nearly impossible to stop such acts of violence without good intelligence.
Someone snooping around trying to find out how to cast explosion spells or casing soft targets for attack is going to stand out, and your magic anti-terror corps is likely to identify such an individual and keep tabs on them.
Everyone Takes Responsibility for Their Own Self Defense
If everyone is taught magic, everyone is going to know how to construct defensive spells. Are you the owner of a restaurant and want to protect it from magical terrorism? Hire a professional to place magical wards of protection on your store. Some of the wards might warn of someone with evil intent, some might protect against certain types of explosion magic, others might dampen mana altogether making it difficult for people to cast magic in the first place.
Every avenue of attack has a counter, and people cast protection wards on themselves and their houses as a matter of fact. To them it's as common as locking your door at night, or dressing appropriately for the weather. People just do it as common sense.
As an aside, we have a lot of situations like this in real life. Besides the chemistry example, anyone can learn to code, and anyone can learn to hack, yet we don't have worms and viruses making life on the internet impossible. Everyone has access to kitchen knives, yet we're not all stabbing each other in the streets. There will always be bad actors, and there will always be ways of stopping them. It's a question of white hats vs black hats, and in general people are conformists to society, so there will always be more white hats than black hats in a given situation.
The difference here is it's hard to get an advantage over anyone because everyone is taught magic. So in that case, you already have an answer of how to stop people from abusing the system: education and equipment, risk vs reward. Criminals are deterred by the risk vs reward, namely that if they attack someone, there is a risk they will be overpowered by that person's magical knowledge. Since it's impossible for the criminal to know who he or she is facing, he or she must assume everyone is dangerous since everyone knows magic. Your deterrent is built in by society's education.
Criminals are in general cowards who are only violent when they feel they have an overwhelming advantage. Often when their victim pushes back they have no idea how to respond. A criminal is more confident with a gun or knife because that criminal assumes no one they face is likely to have one. When met with force, they almost invariably panic and retreat, even if their weapon has them at a distinct advantage. In most cases the criminals will likely use magic that lets them get away with their crime with the least personal risk. Muggers are likely to be less of a problem than magical pickpockets. A mugger has to assume that literally everyone they face has the ability to fight back with magic, so they will act in groups or with strong confidence. If all the criminal wants is your money, it's safer to say, use a magic spell that allows them to teleport your wallet out of your pocket. This situation maximizes the reward to the criminal while minimizing the risk. It doesn't matter how powerful their victim is, if that victim doesn't know they're under attack they can't act.
In addition, people are less likely to play the victim if the criminal has no means of intimidating them with some kind of advantage. If a 5'2" 70 pound kid walks up to you and demands your wallet, you probably won't give it to him. If the same kid walks up and points a knife at you, you're more likely to do so. If that same kid does it with a knife but now you have a gun, you're not going to hand it over this time. This is the deterrence of your magic society. Literally everyone is walking around with a gun and the understanding of how to use it.
The real dangers in your magical society will be the same as in ours: mentally unstable people who don't value their own lives. These types of people are going to lash out no matter the situation using whatever means are available and don't follow the rules of normal deterrence, but in your magic society there is a difference from ours: everyone is taught the means to defend themselves as easily as we're taught to read and write. The crazy actors will still act, but they will be quickly stopped by those around them.