Edit: To be clear, I'm not asking for court cases or legal code citation (though I'd gladly accept them.) I'm just looking for a broad overview of the subject, since most discussions I've had about it are very contradictory.
Okay, avoiding court cases and legal code citations, going by my "very much not a lawyer" self defense training classes:
1. The first question would be "where and when?" You need to know the state and time because, well, the laws involved vary by state and time.
2. It is indeed less "arrest" and more "detainment until the cops get there"
3. Remember that improper detainment can also be called "kidnapping", which by most state laws only means that you prevent somebody's free movement. Assault, Battery, and more are also options depending on what you do.
4. Proportionality can be a concern. It's one thing to do a flying tackle followed by a few head smashes into the concrete if you just did it to a wannabe spree shooter, it's quite another to do it to a suspected shoplifter.
5. Generally speaking, you're only allowed to "detain" suspects long enough for the police to get there if you actually witnessed the crime(and over a remote video camera isn't good enough), the crime is
serious(trespassing into an empty house under construction isn't), and you need to do so otherwise critical evidence of the crime will be lost, or you have a
very good reason to believe that (more) violence and injury/death will occur if you don't detain them. Again, more is allowed for, say, murder, than shoplifting.
6. Better hope that the prosecutor likes you a whole lot better than the person you just detained.
etc...
But as
@GamingGeek mentions, this is Marvel, and thus the laws may be different.
Edit: Going back to my vague memories of spiderman, I remember him often busting what appeared to be "known criminal #5" with what would presumably be very illegal guns in NYC. With plenty of non-spiderman witnesses to them employing said guns in criminal manners.
Which would elevate "tie up and leave for police" to be an actually reasonable thing to do under "self defense"* and "citizen's arrest" type laws, with the main problem being refusing to be available to give a statement to police.
*Self defense can include the defense of others! Criminals waving firearms around a threat to everybody around them...