The Pentagon's inspector general explained yesterday how the Pentagon can lose $1.6 billion through waste and inefficiency:

* The Army spent $252,000 two years ago to install new boiler systems and improve parking lots of buildings slated for demolition.

* The Naval Air Systems Command paid $2 million to repair defective weapons parts between 1982 and 1984, ignoring contract provisions that might have held defense contractors responsible for the repairs.

* The Air Force ordered equipment worth $500,000 for the Titan missile storage area, which is expected to be closed down soon.

Inspector General Joseph H. Sherick summarized internal audits for the six months ending March 31 in his semiannual report to Congress, released as lawmakers considered President Reagan's $300 billion defense budget.

Pentagon officials pointed out that the waste and inefficiency were discovered by the Pentagon and that contract officials have agreed to "corrective actions" expected to save $790 million.

Some of the largest examples of waste and inefficiency were uncovered in management of the largest weapons systems. The Pentagon, for example, failed to charge foreign governments for the costs of improving U.S. fighter aircraft sold to them -- costs expected to reach $278.3 million over the life of the contracts.

The Navy agreed to pay Newport News Shipbuilding and Dry Dock Co. higher labor rates for the construction of Trident submarines than projected by the Pentagon index, handing a potential windfall of $6.9 million to the contractor.

Unnecessary stockpiling was cited as a common problem, with two Army divisions in Europe compiling $174,000 worth of excess supplies that were in critically short supply elsewhere.

In another case, the Army had developed and is planning to buy a new battery for its single-channel ground and airborne radio system despite having a suitable charging system in its inventory, Sherick said. Using the new battery would cost an extra $76.7 million.

The Air Force had been planning to buy 136 new aircraft engines even though it had more of the engines than it needed.

The Navy had nearly doubled its inventory of uniforms, spending an excess of $8.8 million that could have been drawing investment income or used for other projects.

All of the services were blamed for over-ordering certain spare parts by failing to count in their inventories those parts being repaired in contractor plants. Of $123.5 million worth of spare parts sought in the fiscal 1983 budget, $25 million were on hand.

Sherick criticized the lack of The Air Force orderd equipment worth $500,000 for the Titan missile storage area, which is expected to be closed down soon. competitive bidding in several contracts.

The Air Force, according to the report, will spend an extra $58 million by refusing to have competitive bidding for parts of the Advanced Medium Range Air-to Air Missile (AMRAAM).

The Defense Nuclear Agency was blamed for hiring contractors to study technical projects, then awarding the work to them without competitive bidding.

Another costly problem uncovered by Sherick is unneccessary construction.

In addition to the $252,000 paid by the Army for new boilers and driveways, it spent $510,000 to renovate 27 temporary structures, eight of which were scheduled to be torn down.

The Army also spent $1.2 million to pave a runway, taxiway and parking lot at an airfield. Four months later, however, the airfield had so deteriorated from bad work that landings were restricted.