THE 4TH POLICE District of the Metropolitan Police Department is establishing quite a name for itself--and it isn't good. As the most populous of the city's seven police districts, 4-D--which stretches north from Columbia Heights in Northwest Washington to the Silver Spring line--is host to both grand homes and impoverished apartments. The district also has several cops in trouble.

The list of officers accused of being on the wrong side of the rules just since November is stunning:

* A 10-year member removed from the vice squad in December on complaints of taking money from people.

* A police sergeant convicted in November of stealing $1,600 worth of perfume while investigating a crime, and then selling it to other officers.

* A nine-year veteran charged in December with two counts of armed robbery--namely, holding up customers of prostitutes while in uniform.

* A seven-year veteran stripped of his badge and gun on Jan. 4 after being accused by Fairfax County Police of looting a self-storage unit and making off with thousands of dollars of property.

The 4th District's commander, Melvin Scott, who was put in charge in November 1998, was demoted to captain last November after failing to deliver a report on an investigation of money that--guess what?--disappeared from a 4-D safe that had been left open. A new commander was named yesterday; 4-D residents have the right to demand improvements, and soon.

This is a police district that was leading the city in burglaries and robberies when Mr. Scott arrived on the scene. It is also building a reputation for sloppy police work, as when an officer and a detective failed to search the house where a woman was found strangled last October; actually, they thought she had died of natural causes. Police were called back to the scene by family members who smelled a foul odor. Only then was the body of a second woman found--shot to death.

Police Chief Charles Ramsey is said to be outraged by evidence of sworn officers who dirty their own badges and perform sloppy police work. He should be; corruption and incompetence make for a dangerous combination. But more than outrage is called for. The chief must rid the ranks of corrupt and incompetent police officers who stand in the way of making the Metropolitan Police Department a first-rate police force. He owes it to the public--and to the majority of dedicated officers who literally put their lives on the line every time they step out on the streets to do their jobs. This week, Chief Ramsey announced another sweeping department reorganization. That could be a good start.