Eight witnesses testifying about matters ranging from air conditioning repair to an encounter with a Hollywood celebrity took the stand at the corruption trial of former Virginia governor Robert F. McDonnell and his wife, Maureen — sending the already wild proceedings into a realm even more bizarre.

In between, new details were revealed about other aspects of the aggressive investigation of the former first couple and Maureen McDonnell’s alleged attempts to throw off the probe.

[Follow our liveblog for the latest]

The McDonnells stand accused of conspiring to sell the prestige of the governor’s office in exchange for more than $150,000 in luxury items, vacations and loans from dietary supplement executive Jonnie R. Williams Sr.

Steven Spielberg got an unexpected mention as a Virginia Commonwealth University cardiologist testified that he was taken by Williams to the Virginia governor’s mansion in October 2011 and walked into a reception honoring the famed director and his movie “Lincoln.” The movie was filmed in Virginia and embraced by the McDonnells.

List of gifts given to the McDonnell family from Jonnie Williams.

At the time, Williams was trying to persuade the doctor to do research on a new dietary supplement made by his company, Star Scientific, and had told the doctor in advance only that they would meet to discuss a possible study.

After parking on the mansion lawn, Williams, with Maureen McDonnell, zipped the doctor to the front of a line waiting to meet Spielberg and the two exchanged pleasantries.

“This was the most unusual event that you can imagine,” said George Vetrovec, the cardiologist, when asked to describe what he told colleagues after the incident. “You just never know what’s going to happen every morning when you wake up.”

The testimony came as prosecutors continued trying to build a public corruption case against the McDonnells, arguing that the couple gave Williams unusual access in exchange for his financial assistance.

But the bulk of the day’s witnesses provided testimony regarding related charges that are pending against the former first couple — that Maureen McDonnell engaged in obstruction of justice after learning of the investigation and that the couple lied on financial documents by omitting references to loans they had received from Williams.

When she was first interviewed by two state police investigators in February 2013, Maureen McDonnell said she had a written contract with Williams about a $50,000 loan, that she was making periodic payments and that Williams was a longtime family friend, the investigators testified. None of it, prosecutors say, was true.

Prosecutors also showed jurors evidence Tuesday that Maureen McDonnell tried to mislead investigators about her dealings with Donnie O. Williams — Jonnie Williams’s handyman brother. In 2012 and 2013, he worked on air conditioning, hardwood flooring and landscaping at the first couple’s suburban Richmond home. He also replaced the Jacuzzi cover.

Speaking with a thick drawl, Donnie Williams acknowledged that Maureen McDonnell had offered to pay for the work several times. But she also made no objection when he told her in a December 2012 text message that his brother planned to buy the new Jacuzzi cover that she wanted.

“OMG! I did not expect him to do that,” she responded in a text displayed for the jury. “Thanks Donnie!”

Donnie Williams, a former sheriff’s deputy, testified that the first lady insisted on being billed for his work only after the investigation became public, and even then, he said, he provided her an invoice created in “a couple minutes,” charging deeply discounted rates. E-mails show that she asked for the invoice March 4, after the first lady knew of the probe but before it had become news.

The governor, Donnie Williams said, never asked for a bill, though he knew at least of the air conditioning work. Of the first lady’s eventual payment, Donnie Williams said: “I wasn’t even going to cash it. I didn’t even want anything to do with any of this mess.”

Donnie Williams testified, too, that the first lady asked him in March 2013 to deliver a box with a note and dresses inside to his brother.

Jurors now know that Jonnie Williams purchased the clothing for Maureen McDonnell during a 2011 shopping trip to New York City and that he claims it was never part of the plan for him to get them back.

Donnie Williams said that the first lady was “nervous” as she gave him the box and that, at some point, she brought up the investigation that was then closing in on her, her husband and Jonnie Williams.

“She was upset, and she said she was going to call the FBI agent up and tell him Jonnie’s a generous person and they shouldn’t be doing this,” Donnie Williams testified. “It just didn’t make any sense.”

Defense attorneys have pushed back against the idea of a coverup and did so vigorously Tuesday. When questioned by defense attorney William Burck, a state police investigator, Charles Hagan, acknowledged that he did not tell the first lady she was being investigated during the February 2013 interview, nor did he tell her that she had the right to remain silent and the right to an attorney.

Also under Burck’s questioning, Hagan acknowledged that his notes from the interview do not precisely match his memory of what Maureen McDonnell said. He testified, for example, that the notes refer merely to a “contract” about the $50,000, not a written one.

He also testified that the notes do not include the phrase “periodic payments,” only the words “paying back.”

Hagan also testified about aggressive steps taken in the investigation that the jury might find distasteful. He acknowledged, for instance, that at one point he tailed Chris Young, who is married to one of McDonnell’s daughters. He also said he accepted tips on the case from a member of the governor’s state police protection detail.

The day concluded with testimony from William D. Sessoms Jr., the mayor of Virginia Beach and the president of Towne Financial Services Group.

Sessoms, who has been friends with Robert McDonnell since the late 1980s, testified about the former governor’s troubled loan history with Sessoms’s bank. He said McDonnell had repeatedly incurred late fees on loans he had taken out with his sister on two investment properties.

McDonnell also had trouble securing long-term, low-interest financing for the homes because their value had dropped precipitously after they were purchased in 2005 and 2006, Sessoms said.

Sessoms testified that in 2012 McDonnell filed a personal financial statement in hopes of renewing one of the loans but did not list any debts to Williams, who had lent $50,000 just a month earlier to the small real estate partnership that managed the properties.

Ian Shapira contributed to this report.