Derek Chauvin was convicted last month of second-degree unintentional murder, third-degree murder and second-degree manslaughter in the May 25, 2020 death of Floyd.
Evidence at trial showed Chauvin pressed his knee against Floyd's neck for 9 1/2 minutes as the black man said he could not breathe and went motionless.
Defence attorney Eric Nelson cited many reasons in his request for a new trial.
He said Judge Peter Cahill abused the discretion of the court and violated Chauvin's right to due process and a fair trial when he denied Mr Nelson's request to move the trial to another county due to pretrial publicity.
He also said Mr Cahill abused his discretion when he denied an earlier request for a new trial based on publicity during the proceedings, which Mr Nelson said threatened the fairness of the trial.
Mr Nelson also took issue with Mr Cahill's refusal to sequester the jury for the trial or admonish them to avoid all media, and with his refusal to allow a man who was with Floyd at the time of his arrest to testify.
Mr Nelson asked the judge to impeach the verdict on the grounds that the jury committed misconduct, felt pressured, and/or failed to adhere to jury instructions, though the filing did not include details about that assertion. To impeach a verdict is to question its validity.
The brief did not mention recent reports that one of the jurors participated in an August 28 march in Washington, DC, to honour Martin Luther King Jr.
That juror, Brandon Mitchell, has defended his actions, saying the event was to commemorate the 1963 March on Washington and was not a protest over Floyd's death.
Floyd's brother and sister, Philonise and Bridgett Floyd, and relatives of others who had been shot by police addressed the crowd at the march last summer.
Mr Nelson did not immediately return a message seeking details on his allegation of juror misconduct.