Some individuals who have participated in offering cellular radio application services have had legal problems in the past concerning other business ventures, according to law enforcement authorities and documents.

*Washington lawyer Lee G. Lovett was convicted last week of mail fraud in a 1980 bribery case involving the former mayor of an Illinois resort community.

He was found guilty on two mail fraud counts involved in an alleged scheme to bribe the mayor of Fox Lake, Ill., in exchange for help in winning a cable franchise. Lovett was acquitted on a single count of conspiracy to bribe and three counts of interstate travel in furtherance of bribery. Lovett plans to appeal the conviction.

''We believe he is going to be exonerated when the proceedings are over,'' said Joseph Hennessey, a partner of Lovett in the law firm of Lovett, Hennessey, Stambler & Siebert. Lovett was unavailable for comment.

Cellular Application Services, in which Lovett and Joseph Hennessey are partners, sold application services but has recently stopped. Hennessey said that the company is reassessing its business because of the new FCC regulations.

*The Michigan Attorney General's Office two years ago brought a civil suit against Joseph Steingold, who was then president of Salem Mortgage Co., and others for ''usury, fraud and deception in consumer lending and mortgage transactions,'' said Luis Fernandez, an assistant attorney general.

''We claimed that not only was the interest rate to consumers too high, but consumers were deceived regarding the terms of the mortgage transactions,'' said Fernandez.

Steingold denied the allegations and said ''the bottom line was there was no usury. We lowered all of the rates . . .'' and settled the suit for $25,000 with no finding of liability.

Steingold is an independent broker under contract to American National Cellular. He solicits financial planners on behalf of the company. The planners then sell application services to consumers.

Regarding the civil suit, Steingold said ''I'd like to know what that has to do with cellular.''

''We were aware of Mr. Steingold's difficulty,'' said Jerry Dobin, former marketing director of American National Cellular, based in Los Angeles. The company has judged Steingold ''to be of the highest integrity,'' he said. ''Since the allegations are nothing but allegations . . . there was no reason to forfeit his making al iving with us.''

*Robert L. Prince, deputy director of the Alabama Securities Commission said in December 1984 the commission issued a temporary cease-and-desist order against kent Maerki and his company. Spectra Financial Network of Reno, Nev., for alleged violations of securities laws in connection with the sale of interests in a partnership to develop computer software. An investigation is outgoing.

Maerki said ''our law firm . . . was to preregister an offering in Alabama and they did not . . . We were completely in their hands.''

Maerki's company has been marketing the application services of Cellular Corp. of Cleveland since November, 1984.

Nicholas R. Wilson, president of Cellular Corp., said he was unaware of the Alabama matter.

The Securities and Exchange Commission and Maerki last year agreed to an injunction prohibiting Maerki from violating registration and antifraud provisions of the federal securities laws while promoting a company called FoodSource. Maerki agreed to the court order without admitting or denying any of the charges.

''We entered into a settlement of consent, nobody admitted anything,'' Maerki said.

Cellular Corp.'s president, Wilson, said he was generally aware of the SEC matter concerning FoodSource and that no determination of wrongdoing was made against the company or Maerki.

*Cellular Corp. President Wilson himself was the subject of an SEC consent order obtained in 1981. The matter was settled without any determination of wrongdoing when he agreed to refrain from selling securities for one year. The SEC had charged that he broke federal laws covering the purchase and sale of stock options.

Wilson said the SEC matter ''has nothing to do with cellular. It's totally not relevant.'' Wilson said cellular applications are not securities because what is sold is a service, not a portion of an application that will be controlled or managed by another company on behalf of an investor.