United Airlines' application to acquire Pan American World Airways' Pacific Division for $750 million will provide an enormous test for the Transportation Department, whose top political and career officials were hoping to be able to concentrate on winning congressional approval for the Conrail sale.

Many matters in the department have gone on the back burner during the Conrail fight, but this one can't. The law requires the department to act within six months of the application date, April 22.

Secretary Elizabeth Hanford Dole's department assumed oversight of such transactions in January, when the Civil Aeronautics Board went out of business. This transaction, potentially the biggest in civil aviation history, is a tough one to cut teeth on.

The case involves not only airline takeovers or mergers but also trickier issues that surround international aviation.

United and Pan Am want to paint the transaction as a simple business deal involving the sale of assets, the sort of thing that should have minimal, if any, government scrutiny.

But those assets include something that only the president can award a company -- exclusive authority to fly between the United States and another country. United's domestic competitors might question whether an international route award can be sold like an airplane or another asset.

Another problem: technically, if the Transportation Department and then the president approve the deal, Pan Am's Pacific route authority will be canceled and re-awarded to United. Then the president would inform Japan and the other Pacific nations Pan Am serves that United is the U.S. carrier.

However, before United could land at Tokyo on a route once flown by Pan Am, Japan would have to grant landing rights. Japan has made airlines wait years for landing rights after they won route authority from their own governments.

Tokyo is an important hub in Pan Am's Pacific operation and would serve the same function for United, a stronger competitor for Japan Air Lines. Mitsuhiro Kusumi, a Washington representative for Japan Air Lines, called United a "giant competitor" and said its expansion in Japan to include Pan Am's routes would "have to involve some quid pro quo."

He noted that Pan Am has limited service within the United States, concentrated in the East, and little ability to feed its own Pacific routes. United, on the other hand, is the largest airline in the United States and is exceedingly strong in the West. In short, Japan Air Lines might lose passengers it now delivers to United at Los Angeles, San Francisco or Seattle.

This is coming at a time of great tension in U.S.-Japanese trade relations. The announced agreement yesterday on an aviation treaty between the United States and Japan is by no means the final word in the United-Pan Am deal. MOTOR CARRIER SAFETY . . .

One of the orphans in the department is the Bureau of Motor Carrier Safety (BMCS), buried deep in the Federal Highway Administration (FHWA), where pouring concrete is a specialty.

The bureau is supposed to write and enforce federal safety regulations for truckers and has done so in an uneven and unpredictable way, the General Accounting Office recently told Congress.

Dole, in her fiscal 1986 budget, proposed moving the bureau to the National Highway Traffic Safety Administration (NHTSA), but recently dropped that idea in favor of giving the BMCS more visibility in the highway agency. She would do that by appointing an associate highway administrator to head the bureau instead of an office director.

This is just one of several proposals around town on how best to regulate the trucking industry. The American Trucking Associations, the big lobby, would like to see a Motor Carrier Administration created within the department, because the ATA feels it cannot compete for Dole's attention effectively with the railroads and the airlines, which have the Federal Railroad Administration and the Federal Aviation Administration. Dole, however, has shown no enthusiasm for the ATA plan.