A CONTINUING federal investigation of the District's much-criticized Bates Street housing redevelopment project has yielded its first criminal conviction. George Holmes Jr., who was hired to run what became the District's most ambitious redevelopment effort, has pleaded guilty to an income-tax charge of failing to report the salary and fees he took out of the housing project in 1980. Mr. Holmes has agreed to cooperate in a grand jury investigation of the Bates Street project. Federal prosecutors say it is a major break in their case and that charges are likely to be filed against others involved in the project.

Bates Street was to have been the showcase effort of Mayor Marion Barry's 1978 campaign pledge to restore abandoned inner-city housing. It was a symbol that cost $13 million for 163 units, the most expensive redevelopment effort ever undertaken by the District. Now the possibility of more convictions hangs over the project. The project is still not completed. Some residents are satisfied, but others complain of serious construction flaws and slow and shoddy repair work, and threaten to take their claims to court.

Bates Street has after seven years indeed become a symbol for the District government -- of the wrong way to run a redevelopment project and the wrong way for a city government to investigate a project gone wrong.

In 1982 D.C. Auditor Otis Troupe reported that nearly $4 million in interest-free government loans to the project was unaccounted for. This startling news was not met with any kind of serious internal probe by the District government. Two years later, this newspaper published a series of stories documenting mismanagement, improper use of project funds for personal gain, shoddy bookkeeping, instances of multiple payment for the same work, and other problems plaguing the project. These were serious charges. Mayor Barry wrung his hands. There was nothing he could do about it, he said. Those folks did not work for him anymore.

In the absence of decisive District government action, a congressional subcommittee spoke out about the seriousness of the case and called for a grand jury investigation. And, having taken no action on his own, Mr. Barry then decided to criticize the speed of that federal investigation.

The investigation gained some steam this week. The full story is far from clear, but the investigation has already demonstrated that the shortcomings went beyond simple poor management. That is a very good reason for pushing it farther along, with or without the mayor's help.