Construction is nearly completed on the 13.8-mile extension of the Red Line from the Van Ness-UDC station on Connecticut Avenue NW to Shady Grove in Montgomery County, and officials are now debating when to begin service.

Because of delays in deliveries of new rail cars, Metro officials have said they do not expect to have enough cars to open the entire Shady Grove extension until late 1984. But a portion of the new branch might open earlier in the year, officials have said.

One initial proposal was to start service in mid-1984 from Van Ness-UDC to the Grosvenor station near Rockville Pike south of Tuckerman Lane. Because of complaints from residents in nearby communities about a prospective influx of commuters, Montgomery County officials began examining whether the White Flint stop north of Nicholson Lane might also serve as a temporary terminus. More parking spaces are available at the White Flint stop than at Grosvenor.

In addition, neighborhood groups in Northwest Washington recently urged the transit authority to open the Friendship Heights station at Wisconsin and Western avenues as an interim terminus. D.C. City Council member Jerry A. Moore Jr., a Metro board member, has asked the authority to study this proposal.

The suggestions have raised several other issues, including what changes might be required in bus routes near the new rail extension. Fares have not been set for the Shady Grove branch. Nor have transit officials calculated what the additional service might cost, how frequently trains should run or how many passengers are likely to ride them.

Moreover, Montgomery County officials have expressed concern about proposals that might result in less service to Shady Grove than to other Red Line stations closer to the District. Fares to Shady Grove probably will be high, county officials have argued, and commuters are unlikely to be attracted to the rail system unless service is frequent.

Trains are already testing tracks along the extension, and most of the work remaining to be completed appears relatively minor.

With electric power along the extension now switched on, Metro officials have expressed concern about several incidents in which intruders cut through metal fences and apparently walked across rail tracks near Frederick Avenue in Montgomery County. The 750-volt third rail beside the tracks poses a hazard, officials warned.

At the Red Line's other end, workers have largely completed the concrete foundations of the Forest Glen station north of the Capital Beltway near Georgia Avenue, and a construction contract is expected to be awarded soon to extend the line to Wheaton.

So deep is the Forest Glen station that the transit agency plans to install high-speed elevators, instead of escalators. Six 200-foot shafts have been built. As a precaution, diesel engines will be installed for use if an elevator's motor breaks down, officials said.

The transit authority has tentatively planned to extend the Red Line from its present Silver Spring terminus to Forest Glen and Wheaton in 1988 and to Glenmont in 1990.

Metro officials recently warned, however, that a Senate move to hold down spending for subway construction may result in a year's delay in the Wheaton station's opening. In addition, the Reagan administration has not agreed to provide funds for the extension to Glenmont.