In Florida, it is illegal to pay someone per registration form.

“I told my friends in the party then that paying people to do this was a bad idea, and it almost inevitably leads to problems,” Mr. Lux said. “Unfortunately, I was not proven wrong.”

Fred Petti, a lawyer for Strategic Allied, said the employees were paid only by the hour, with no quota attached. He added that they also were instructed to register anyone from any political party, not just the Republican Party.

Previous investigations of Mr. Sproul’s operations focused on efforts to register only Republicans or allegations that Democratic forms were torn up. Mr. Petti also said that Mr. Sproul cooperated with the Palm Beach County election supervisor to find out who was at fault and has offered to do the same with other election supervisors.

In Palm Beach County, one person was responsible for the fraudulent forms, officials said. Mr. Petti said he does not yet know how widespread the problem is in other counties.

Election supervisors said they have come across forms with handwriting that did not match previous registration forms, bogus addresses and other identifiers like driver’s license numbers that appeared to be invalid. But in other cases, the forms were just incomplete, which does not constitute fraud.

“Until we see what the cards are, it’s hard for us to comment,” Mr. Petti said.

Mark Anderson, the Bay County supervisor, said he has found eight questionable forms in his county, but he is looking for more. The forms had either unchecked boxes for party affiliation or signatures that looked different from previous ones. He said he had also received calls from voters who said they had not changed their party affiliation, although it appeared they had. “I don’t believe there is going to be massive numbers,” Mr. Anderson said.

Election supervisors are able to pinpoint the group responsible for the questionable forms because of a 2011 state law that tightened rules on voter registration groups. The law, which sparked lawsuits and controversy, requires groups to register with the state and have their registration number on the forms they distribute.

A provision that required groups to turn in registration forms within 48 hours was struck down in court this year. “The Republican Legislature was beaten up pretty badly, partially by myself,” Mr. Lux said. “But they seem to have been doing something to improve the process.”