NEW YORK, JAN. 16 -- Mayor David N. Dinkins (D), after a year of plugging budget gaps, today proposed a record $29.3 billion spending plan for fiscal 1992 that includes $580 million in new or higher taxes and 16,500 layoffs.

"No one is going to be happy with this budget," Dinkins said. "Everyone is going to complain to some degree."

The budget, which requires City Council approval, calls for increased taxes on property and income and a new auto tax. It would cut back arts funding and delay hiring new police officers.

Among those unhappy with the plan was schools Chancellor Joseph Fernandez, who denounced it because 4,800 teaching jobs might be lost. "Cuts of this magnitude are tantamount to mortgaging our children's future," he said.

Besides the 16,500 layoffs, 7,900 other jobs would be lost through attrition. The Board of Education will take the heaviest hit, with about 5,000 job cuts in the current fiscal year and an estimated 8,000 in fiscal 1992, which starts July 1, Budget Director Philip Michael said.

Dinkins said that, since he assumed office a year ago, the city has closed budget gaps through 1992 totaling $6.8 billion. "Only 20 states have annual budgets bigger than the hole we already have filled," he said.

Among the cuts would be an estimated 1,996 positions in libraries, contract agencies and the Health and Hospitals Corp.

Dinkins, who closed three fire companies in the past month, said the Fire Department will lose no more companies, but held out the prospect that if the economy worsens, that could change.