Disclaimer: I am not a lawyer. At all. This is just my understanding.
Depends on where you live. Where I live, a civilian’s powers of arrest are basically limited to situations where you directly witness someone committing an indictable offence (i.e. assault, robbery etc), a dual offence (i.e. shoplifting), a property crime (B & E, vandalism etc) or situations where you are assisting someone who you reasonably believe has lawful authority to arrest (i.e. police officer, store security etc.) or the person is escaping from the law. Like I said, this is how it is where I live and it may or may not be the same for you.
As for your examples,
Cell phone guy is arrestable.
If practical ask the cop before intervening, but you are justified.
As for naked guy, where I live public indecency/lude acts etc is not indictable and therefor not within a civilian’s powers of arrest unless it escalates to sexual assault. In other words no, you cannot punch out or even detain the guy jerking off in the bushes at your kid’s school or the naked guy in the park unless he touches someone. All you can do is call the cops and keep eyes on him However, even if he were arrestable, punching him would potentially get you into trouble if that amount of force was not necessary in order for you to safely affect the arrest. What I mean is if grabbing his arm would get the job done, punching is not legal. You need to be able to articulate to police (through you attorney) and potentially later to a jury why your/public safety demanded that level of force in order to affect a lawful arrest. In other words, the bad guy’s behaviour needs to be violent enough to warrant whatever violence you inflict upon him.
Grab-ass guy may be arrestable for sexual assault but again, you would need to detain him with as little force as is necessary to get the job done and call the police and wait. Simply punching him in the face would be assault. That’s really the key. Even if you are within your rights to arrest somebody, “arresting” is all you are within your rights to do. “Putting criminals in their place” is where people get themselves into trouble.
Your knowledge of the legislation where YOU live and your ability to articulate your actions after the fact and take intelligent steps to protect yourself legally after the fact (i.e. submitting your statement to police at a later time through an attorney etc.) will often have as big an impact on the outcome as your actual actions.
We should not be afraid to take action, but understand that even if you do the “right” thing and sometimes even the lawful thing you take a risk, both physically and legally. If you understand and are willing to accept that risk and do the right thing anyway, good on you, IMO.
Edit - I believe that you also need to tell someone that you are arresting them and why and provide them with a reasonable opportunity to surrender before you apply force, unless some immediate threat prevents this. In other words you need to tell cellphone guy to stop before you tackle him and you need to tell grab-ass guy that he’s being arrested for sexual assault before you lay hands on him. You need to give some kind of lawful commands and allow the person the chance to comply. If you fail to do this you are not affecting a lawful arrest. With the cop in the fight or some other immediate threat of physical harm coming to somebody, you can take more direct action if needed.
