As President Trump posed triumphantly for photos with police officers, government agents and members of the National Guard in Southeast Washington last week, lawyers across town in federal court grappled with his new brand of justice.

The stream of defendants who shuffled through a federal courtroom on Thursday afternoon illustrated the new ways in which laws are being enforced in the nation’s capital after the president’s takeover of the city’s police. They were appearing before a magistrate judge on charges that would typically be handled at the local court level, if they were filed at all.

One man had been arrested over an open container of alcohol. Another had been charged with threatening the president after delivering a drunken outburst following his arrest on vandalism. And one defendant’s gun case so alarmed prosecutors that they intend to drop the case.

Mr. Trump has cast his crackdown on crime as a success, and suggested on Friday that it was a blueprint he would seek to apply to other cities, including Chicago. To defense lawyers and even some prosecutors, though, many of the cases that have landed in court have raised concerns that the takeover seems intended to artificially inflate its effect because government lawyers have been instructed to file the most serious federal charges, no matter how minor the incident.

One of the recipients of Mr. Trump’s show of force was Mark Bigelow, 28, a part-time delivery driver for Amazon.

After midnight on Aug. 19, Mr. Bigelow was sitting in the middle row of a van parked on a street in Northeast Washington with its doors open, according to court papers. Two other men were in the front when a full complement of law enforcement officials — from the Metropolitan Police Department, the F.B.I., the Drug Enforcement Administration, Immigration and Customs Enforcement and the State Department’s Diplomatic Security Service — stopped and saw what appeared to be an open container of alcohol in the front seat.

As law enforcement questioned and searched the two other passengers, Mr. Bigelow left the van and started to walk away, until other agents stopped him, according to the charging document. Peering into the van, an officer spotted “a second cup containing an alcoholic beverage in the middle row seat,” at which point Mr. Bigelow was arrested on charges of possession of an open container, a misdemeanor.

As he was placed in a vehicle, the handcuffed Mr. Bigelow became belligerent, twisting his body and yelling, “Get off me! Y’all too little, bro!” at an ICE agent, according to a court filing, which described how Mr. Bigelow made “physical contact” by kicking an agent in the hand and another in the leg.

As a result, Mr. Bigelow was charged with assaulting, resisting or impeding a federal officer, an offense that carries a maximum sentence of eight years in prison.

The charges follow a directive by the U.S. attorney, Jeanine Pirro, to prosecutors to charge the most serious crimes possible in each case and to do so in federal court, where sentences tend to run much longer.

A federal public defender representing Mr. Bigelow, Elizabeth Mullin, told the U.S. magistrate judge, Moxila A. Upadhyaya, that he would never have been arrested, let alone charged with a federal felony, but for the president’s crackdown. “He was caught up in this federal occupation of D.C.,” she said. “This was a case created by federal law enforcement.”

Next up was Torez Riley, 37, who was arrested at a Trader Joe’s grocery store for what the police said was possession of two handguns in his bag.

Mr. Riley’s case has been a point of contention inside the U.S. attorney’s office, where a number of prosecutors concluded that officers unlawfully searched Mr. Riley when they stopped him, violating the Fourth Amendment, according to people familiar with the case who spoke on the condition of anonymity to discuss internal deliberations.

Before Mr. Trump’s crackdown, prosecutors in Ms. Pirro’s office would have been likely to dismiss a case like Mr. Riley’s after an initial review of the facts of the arrest, according to the people, who were familiar with the instructions.

Those people said that after Mr. Riley’s arrest, Ms. Pirro pushed her subordinates to charge the case despite those concerns. One person familiar with the matter disputed that characterization, saying that the prosecutors handling the case did not have a full command of the facts, and that when she saw the police body camera footage of the arrest on Friday, she ordered them to dismiss the gun charges against Mr. Riley. A detention hearing in the case is scheduled for Monday.

In a statement, Ms. Pirro said: “My job is to prosecute crime in what was one of the most violent cities in the world. In so doing, I will always act with integrity and responsibility. Under my watch prosecutors will be aggressive in getting guns off the street and arguing cases to judges, who make final determinations, but they will do so consistent with the law and the facts.”

The argument for dropping such a case is not simply a question of being tough or soft on crime, or constitutional rights. Prosecutors have to worry, particularly in Washington, that an appeals court could, in throwing out a case like Mr. Riley’s, issue a decision that makes it harder for officers to search people on the street. Such an adverse ruling, they reasoned, could hamper crime-fighting efforts for years to come.

That was the primary concern of the prosecutors who argued against pursuing the Riley case, these people said.

Mr. Riley made his first appearance in court on Thursday about the same time that Ms. Pirro stood in the sun with Mr. Trump in Southeast Washington.

“I am making sure that we back the blue to the hilt,” she told officers and agents crowded around the president. “Every arrest you make, we’re going the longest way to make sure that we charge in those cases.”

The next defendant was Edward Dana, 30, who is accused of threatening the president’s life, which carries a potential five-year prison sentence.

Mr. Dana, who has a history of mental illness and arrests, was stopped around 10 p.m. on Aug. 17, after the police received complaints that he had damaged a light outside a restaurant in Northwest Washington.

A group of police officers and federal agents arrested him for property destruction. As he settled into the back of a police car, he asserted that he was drunk after having consumed seven drinks. An officer’s body camera captured his comments. He became irate, yelling at the officer driving the vehicle that he would return to the restaurant and beat up someone.

“I’m not going to tolerate fascism,” he declared, vowing to “protect the Constitution by any means necessary. And that means killing you, Officer, killing the president, killing anyone who stands in the way of our Constitution.”

The officer immediately radioed his dispatcher to “notify Secret Service — he just made threats to kill the president.”

Not long afterward, Mr. Dana began to sing. A Secret Service agent reviewed the video of his comments and filed a charging affidavit against him.

“He is not a danger,” his lawyer, Ms. Mullin, told the judge. “The danger here is having federal agents roaming the streets.”

Judge Upadhyaya urged the two sides to reach an agreement on conditions for his release, but as the hearing wore on, she began to lose patience with the prosecutor, Conor Mulroe. Mr. Dana was a menace, he argued, insisting that his mental health problems should not be an excuse to allow him to keep harassing people and businesses.

Mr. Mulroe added that given Mr. Dana’s long history of “quite erratic behavior,” he should remain in jail while awaiting trial.

As the hearing continued, Judge Upadhyaya became exasperated with Mr. Mulroe.

“I know what you’re doing and I just have no tolerance for it,” she snapped. “There has to be a common-sense application of the law.”

Her last case of the day involved a man who had been arrested in Washington based on a warrant in nearby Virginia. Finding no one else able to transport him at night from one jail to another, she persuaded Ms. Mullin, the defense lawyer, to do it.

“The time and resources of the court are stretched beyond belief,” the judge said. “It’s been like this all week.”

Nicholas Bogel-Burroughs and Alan Feuer contributed reporting.