The red diamond sticker labeled "rejected" that every District motorist fears may be waiting at the end of the annual auto inspection line will disappear from windshields next year.

Cars can still fail inspection, but the city can't afford the red stickers any more so they will be eliminated -- a minor casualty of the city's fiscal crisis. The stickers used for vehicles that pass inspection, showing the month in large digits on the front, will be modified for use on rejected vehicles, too.

That is one of dozens of minor items lurking in the small print of the proposed 1982 budget Mayor Marion Barry unveiled last week. Trying to save a dime here, a million dollars there, the Barry administration has been going through city departments looking for even small changes in procedures that might cut costs. The changes at the Motor Vehicle Administration will be among those felt most immediately by large numbers of city residents.

Other changes include these:

New cars will not have to be inspected until they are 2 years old, instead of the present one year. Lawrence Greenberg, deputy assistant commissioner in the motor vehicle department, said this change will not have any significant efect on the safety of cars on the streets because "only 3 percent of all cars have been rejected on their first-year inspection." Usually, this has been for mirror defects such as incorrect headlight adjustment.

Learners' permits will be valid for four months instead of two. Greenberg said that because it takes nearly a month to arrange an appointment for a road test, most learners can take the test only once during the time their permits are valid. If they fail, as about a third of them do, they have to renew their permits before they can take the test a second time.

"We get about 18,000 learners' permit renewals a year," Greenberg said. "Most of those people pass the road test the second time, so we just want to allow them to take it twice without having to renew. The advancing for us is the elimination of 18,000 transactions, so we can cut somebody from that department to do something else."

The item in the budget that will probably have the greatest impact on most city residents is "elimination of tag rush overtime." That means that during the annual period when license tags must be renewed, the motor vehicle office will work only normal weekday hours -- a change that is sure to lengthen the lines of surly motorists outside 300 Indiana Ave. NW and the satellite tag-issuing stations.

"We don't feel it has to cause longer lines," Greenberg said. "Not one motorist has to wait in line because they can all renew by mail. What we want to do is encourage more people to renew by mail" to eliminate the need to wait inline.

If the proposed budget is approved by the City Council and Congress, the changes will take effect a year from now, Oct. 1, 1981, the start of the 1982 fiscal year. The estimated annual saving to the city is about $38,000.