What happens when a federal executive is given an assignment and then a dispute arises over spending the money to do the job?

President Reagan has nominated Manuel J. Justiz to head the National Institute of Education, the Education Department's $54 million research agency.

If Justiz is confirmed by the Senate, he will become NIE's fifth chief in 2 1/2 years.

An associate professor of education at the University of New Mexico, Justiz was recommended for the post by Sen. Harrison Schmitt (R-N.M.), whose good will the White House would like to keep -- presuming he survives his reelection battle.

With Justiz moving in, Robert Sweet -- who had been acting director since the abrupt resignation of Edward Curran in June -- goes back to the deputy director's post.

Not getting the job permanently was a defeat for Sweet, a onetime teacher, school board member, salesman for educational publishers and head of New Hampshire Citizens for Morality.

"I was very anxious to be director, but the decision has been made," Sweet said yesterday. "I don't plan to make any moves. I have a presidential appointment here."

The decision to put the 33-year-old Justiz in the job brought sighs of relief from groups like the American Educational Research Association, an umbrella organization whose members do the kind of work viewed with skepticism by Curran and Sweet. Justiz is a member of the group, though he keeps his distance from its management, one AERA official said.