harry potter - How are dark curse users uncovered?

Question behind the question: I was actually thinking about the implications of dark curses: Anyone can use a dark curse on anyone else (provided they are properly educated in magic and so on). For Avada Kedavra and Crucio, that didn't seem too bad. In America, people are allowed to own guns, and abusive people exist. Imperio seems problematic. Anyone can control anyone else? Wow. It's like everyone has a ring of gyges. Perhaps I am cynical, but I highly suspect people would use Imperio if given the chance since they would be unlikely to be caught, or so I assume. Thinking about it more, a lot more people would be dead or abused if their murderers or abusers had higher probability of escaping justice.

The somewhat dumb question: So now I, of course, question my assumptions. How would dark curse casters be caught? In general, how do aurors or anyone catch criminals, solve crimes, uncover mysteries or murder mysteries?

Side question: How do you know anyone is under the Imperius Curse?

I don't think spells can be traced aside from Prior Incantanto, and that's assuming you ever encounter the one who cast the spell.

I'm guessing wizards don't check for DNA or hairs because dark wizards/criminals would likely just say "accio (hair, DNA, evidence, etc)" or something.

Answer

How do Aurors catch criminals?

Very Poorly. Very few Death Eaters are in Azkaban, and only after a string of crimes. Voldemort murdered and stole and did other things for years with no Auror interference or clue. Mundungus doesn't seem to be all that used to the inside of a jail cell either. Knockturn alley has shops doing/selling shady things with nary a Bobby around.

How can Aurors catch criminals?

1. 
   

   Same mundane way crimes were solved in Medieval times by muggles.

   
   
   
   
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     Most criminals (even today) are caught because the blabbed to the wrong person, NOT because of some deeply advanced police work.

     
     
   
   
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     Means, motive, and opportunity. Especially motive. Everyone in a small community knows that Egan the Wandwavey was annoyed the hell by Iglin the GoodLooking getting it on with Egan's wife. So when something funky happens to Iglin, Aurors kinda know who the primary suspect is (and that's where Prior Incantanto comes into play).

     
     
   
   
   
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     Humans produce ~3% sociopaths. Probably wizards, too. So, if something is stolen, Mundungus is kinda the first suspect for the Aurors. If someone is killed, known criminals (Death Eaters) are first suspects.

     
     

     This is circumstantially confirmed when nobody has a first idea to look at Tom Riddle when Hepizbah Smith dies.

     
     
   
   
   
   


2. 
   

   Magic leaves traces.

   
   
   
   
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     We saw Dumbledore trace Voldemort's magic in HBP, at a cave entrance.

     
     
   
   
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     We see wizards are able to identify quacking Undersecretary in PM's office as having been a subject of failed Imperio in HBP.

     
     
   
   
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     In general, healers at St. Mungo need this ability to be able to perform counter-curses.

     
     
   
   
   
   



3. 
   

   Legilimency.

   
   

   You can read a victim's mind and see who was around him.