You are allowed to stop every person you "suspect".
Like I said: Disorderly Conduct and Loitering are two that are used quite often and hard to refute.
You really like circles, don't you?
here is the arizona law in question.
http://www.azleg.gov/FormatDocument.asp?inDoc=/ars/11/01051.htm&Title=11&DocType=ARS
For any lawful stop, detention or arrest made by a law enforcement official or a law enforcement agency of this state or a law enforcement official or a law enforcement agency of a county, city, town or other political subdivision of this state in the enforcement of any other law or ordinance of a county, city or town or this state where reasonable suspicion exists that the person is an alien and is unlawfully present in the United States, a reasonable attempt shall be made, when practicable, to determine the immigration status of the person, except if the determination may hinder or obstruct an investigation. Any person who is arrested shall have the person's immigration status determined before the person is released. The person's immigration status shall be verified with the federal government pursuant to 8 United States Code section 1373(c). A law enforcement official or agency of this state or a county, city, town or other political subdivision of this state may not consider race, color or national origin in implementing the requirements of this subsection except to the extent permitted by the United States or Arizona Constitution. A person is presumed to not be an alien who is unlawfully present in the United States if the person provides to the law enforcement officer or agency any of the following:
1. A valid Arizona driver license.
2. A valid Arizona nonoperating identification license.
3. A valid tribal enrollment card or other form of tribal identification.
4. If the entity requires proof of legal presence in the United States before issuance, any valid United States federal, state or local government issued identification.
so let's break this law down to more normal languge.
For any lawful stop, detention or arrest made by police in the enforcement of any other law, where reasonable suspicion exists that the person is an alien, then an attempt shall be made to determine the immigration status. A person is not a illegal alien if they present ID.
So the police has to first stop you for another law, then there has reasonable suspicion of being an illegal, then the police must try to determine immigration status. So no the police can stop you on just the suspicion of being an illegal immigrant.
http://www.azleg.state.az.us/ars/13/02905.htm
Guide on not to loiter in arizona. Don't be a positute, beg, or gamble in public and leave from schools/bus stops/train stations/airports, if requested to leave.
http://www.azleg.state.az.us/ars/13/02904.htm
Guide on not to commit disorderly conduct in arizona. Don't get in a fight, be loud or offensive, or shot a gun in public. Also follow police instructions in an emergency sititution.
I don't see how your average person commits loitering or disorderly conduct very regularly by arizona standards.
Also let's assume a cop does exactly what you say. In section K, if the cop acted in bad faith then the cop can be held responsible for the cost of his actions. The lawsuits or the threat of lawsuit will quickly kill any bad behavior.
if you're wonder how this law will be enforced without racial profiling, you may wish to watch this training video.
http://www.azpost.state.az.us/SB1070infocenter.htm