The Fairfax County Board of Supervisors yesterday endorsed a recommendation by the staff of the Virginia Department of Highways and Transportation to lift restrictions that limit the rush-hour lanes on Rte. 50 to four-member carpools and buses.

The recommendation, which would allow all vehicles to use the restricted lanes running from Rosslyn to Seven Corners, must be approved by the state Highway and Transportation Commission before any changes go into effect.

About 70 percent of the cars currently using the rush hour lanes are in violation of the restriction, according to the state transportation staff. Periodically, the staff has people stationed on Rte. 50 counting cars and passengers.

"In view of the low bus and carpool utilization of the Rte. 50 restricted lanes, the high violation rate being experienced, and the recent opening of Interstate 66 . . . the department is considering" lifting the restriction, David R. Gehr of the state transportation office wrote in a recent letter to Fairfax officials.

The Arlington County Board is expected to consider the matter in the next month or two.

In February, during one morning peak period, which runs from 6:30 a.m. to 9 a.m., the state transportation department counted 898 cars in the rush-hour lanes of Rte. 50, which is known as Arlington Boulevard at some points. Of that total, 108 were carpools and 22 buses. Another 196 cars without the mandatory four passengers were making right-hand turns from the lanes, which is allowed. But officials believe that many of those cars go on and off Rte. 50, enabling them to violate the restrictions while avoiding the monitoring areas.

The remaining 572 cars were in plain violation of the carpool restrictions.

Carpool usage of the single lanes east and west, which began in 1978, increased steadily, reaching 1,441 vehicles during the morning rush period in 1980. But since last December, when I-66 opened inside the Beltway, the usage has dropped as carpools heading to and from Washington opted for the new interstate.

In March, state transportation officials counted 1,400 carpools during one 2 1/2-hour morning rush period on I-66 near Spout Run. Strict carpool rules are in effect on I-66 during rush hour.

The Fairfax board yesterday also approved the so-called Groveton Redevelopment plan, the first effort by the Southeast Fairfax Development Corporation to rebuild the depressed Rte. 1 area.

A handful of local property owners had objected to the plan, arguing that they did not want to be forced to sell their land. In an attempt to allay those fears, the board agreed to a series of amendments, one of which requires board approval of condemnation proceedings.

In other action yesterday, Democratic Supervisor Martha Pennino of Centreville District told the board that the Health Systems Agency of Northern Virginia, a regional health planning group, late last week asked the state attorney general and the state health commissioner to investigate the operation of Barcroft Institute, a Falls Church nursing home, owned by Hospital Corporation of America.

A former nurse at the Barcroft Institute, A.J. Fairman, alleged in a letter to Democratic board member Audrey Moore of Annandale that elderly people were moved out of the institute to another nursing home in southwestern Virginia so that HCA could use their beds for psychiatric patients. Experts say that psychiatric patients generate more income for hospitals than do elderly patients.

HCA officials said they are reviewing the matter, and declined further comment on it.