Hogwarts
A student of Hogwarts' cannot do much harm whilst they're at school. There are many counter-measures taken to ensure that their practice of magic is safe whilst at school - including:
- Anti apparition/disapparition measures,
- muggle-repelling charms,
- general distance,
- controlled environments, and
- rules and regulations.
Whilst a Student is outside of the school, they are bound by the Decree for the Reasonable Restriction of Underage Sorcery; which utilises a 'Trace' which detects when an underage wizard uses magic. The offence is then investigated and punished accordingly.
Once the young wizard has grown old enough to graduate is a separate matter, but we do know that to perform a range of magical feats, you actually need a licence; such as:
Sneaking into Number Ten
In addition, in order to accomplish your task of sneaking into Number Ten, you might face the following problems:
- Veritaserum is "strictly controlled" by the MoM (plus it is very difficult to brew).
- Polyjuice Potion is extremely difficult to brew and its ingredients are not easy to come by.
- In order to Apparate successfully to a location, one must use the 3 Ds (Destination, Determination, and Deliberation), it would make it extremely difficult to apparate into a location if you don't know where you're going; see How far can a person Apparate?.
Psychopaths
There will always be those who go un-checked and develop psychopathic tendencies; even Dumbledore himself suspected Tom Riddle throughout Riddle's school years (and beyond):
“Did you know — then?” asked Harry.
“Did I know that I had just met the most dangerous Dark wizard
of all time?” said Dumbledore. “No, I had no idea that he was
to grow up to be what he is. However, I was certainly intrigued by
him. I returned to Hogwarts intending to keep an eye upon him,
something I should have done in any case, given that he was alone
and friendless, but which, already, I felt I ought to do for others’
sake as much as his.
-Harry Potter and the Half-Blood Prince (The Secret Riddle)
Voldemort (Tom Riddle) still managed to become infatuated with the Dark-Arts, and many other evil tendencies, how could this have been stopped?
Grindelwald was a very brilliant wizard, he was also Dumbledore's greatest friend (and more); and yet he managed to attend school and despite a wonderful education (at Durmstrang) ended up hurting many in his quest to purify the world and take over (believing that "For the greater good" was ok).
Sorting / Screening
Each student does get sorted into a house. As you mentioned, many students who get sorted into Slytherin do tend to become attracted to the Dark-Arts, but it is not to be said that the house is intrinsically evil; see Is Slytherin Evil?. This is clearly not the fault here.
As mentioned above, Dumbledore pretty much did a "screen" of Tom Riddle's character didn't he? Even deemed him to be noteworthy and a (potential) risk; both to himself and his fellows. But that did nothing to prevent Tom Riddle ultimately becoming the terrorizing Lord Voldemort.
The limitations of screening / sorting is that it happens at a particular time in one's life; things change, people's beliefs and tendencies change (as may their houses; see: Can one's House change?). Do we then screen / sort them every year?
Another limitation is; how do we know that you are going to end up killing/hurting loads of people? the Sorting Hat can determine a witch/wizard's character and personality, but can it determine other things as well (Why wasn't the sorting hat used to prove Harry didn't put his name in the Goblet of Fire?, Could the Sorting Hat Have Told Dumbledore That Harry Was a Horcrux?), but I don't believe it can tell the future of a person's life.
Does Hogwarts put the world in Jeopardy?
No, it provides an environment for young witches and wizards to hone and control their skills, abilities and emotions to be able to use their powers in a positive manner. As Dumbledore tells Tom Riddle:
“At Hogwarts,” Dumbledore went on, “we teach you not only to
use magic, but to control it. You have — inadvertently, I am sure —
been using your powers in a way that is neither taught nor tolerated
at our school. You are not the first, nor will you be the last, to allow
your magic to run away with you. But you should know that Hogwarts
can expel students, and the Ministry of Magic — yes, there is
a Ministry — will punish lawbreakers still more severely. All new
wizards must accept that, in entering our world, they abide by our
laws.”
-Harry Potter and the Half-Blood Prince (The Secret Riddle)
We cannot allow the actions of one (rogue) individual determine that the (Wizarding) education system does not work.
- Can it be improved? Definitely.
- Is it putting the world in jeopardy? No