Less than a year ago, political corruption seemed to pervade Rhode Island. In recent years, the authorities say, it has been the seat of organized crime in New England. Joseph A. Bevilacqua resigned last spring as the state's Chief Justice after a long dispute over allegations that he had ties to organized crime. In 1984 Mayor Vincent A. Cianci Jr. resigned after pleading no contest to charges of assaulting his wife's lover with help from a police officer. 'That Was a Different Period'

Mayor Paolino said residents had overcome the loss of confidence they experienced in those political crises. ''That was a different period - it's gone,'' he said.

Also gone, he contends, is whatever reluctance businesses might have had about coming to Providence.

He says A.T.&T., which built its regional headquarters near City Hall last year and plans to put up to 400 employees in it, has opened a path that other companies will follow to Providence.

He is pinning his biggest hopes for bringing in new businesses on the proposed Capital Center, a 30-acre parcel of land stretching from the foot of the Rhode Island Statehouse almost to the steps of City Hall. The land was once cut off from the city because of the huge expanse of elevated railroad tracks, the ''Chinese Wall,'' that ran through it. Concern Over Skyline

The tracks have been moved, and the Mayor said he wanted to see office buildings, hotels, a new convention center and retail shops in their place, but Gov. Edward D. DiPrete, as well as some state legislators, are worried that the skyline the Mayor envisions may be too massive for the city and may overshadow the Statehouse.

Charles T. Francis, president of Ryan Elliot, a Rhode Island real estate concern, said prospects for the Capital Center depended almost exclusively on out-of-state businesses because Rhode Island itself did not have enough economic growth to support the development.