If convicted of either first-degree felony, Wall, 49, could spend up to the rest of his life in prison.
On Wednesday, defense attorneys attempted to pick apart testimony from a medical examiner, DNA forensic expert and family friend.
The first witness called was Utah medical examiner Erik Christensen, who determined that von Schwedler died on Sept. 27, 2011, from drowning in her bathtub, but said he could not conclusively rule the death was a homicide.
Christensen said wounds on the woman's body were not typical of a suicide. But an elevated level of Xanax in von Schwedler's system and a lack of clear-cut defensive wounds persuaded him to write on her death certificate that the manner of death was "undetermined."
"Her injuries are much more typical of defensive-type wounds, something that occurred in a struggle," Christensen said. "The problem with homicide is, how did she get Xanax in her system? I don't have a good answer for that."
The amount of Xanax in von Schwedler's system was "toxic to potentially lethal," according to an autopsy report. Especially, Christensen said, because she had no prior history of having taken the drug.
But the presence of the antidepressant wasn't enough to fully persuade Christensen that von Schwedler committed suicide, either.
The autopsy of Uta von Schwedler's body revealed several injuries, including bruising to her lips, scrapes to her right cheek, cuts and puncture wounds, several of which Christensen said he had "never seen anything like this in a suicide."
The woman's internal neck muscles also were injured. When prosecutors asked if that could have been caused by a hand, trying to force or hold someone down, Christensen replied: "Could be."
DNA forensic analyst Emily Jeskie was called next. She testified that evidence collected from von Schwedler's bed, where prosecutors allege there was a violent struggle between her and her ex-husband, could be linked to Wall.
But defense attorneys argued that other DNA was present including that of von Schwedler's boyfriend Nils Abramson, who was originally a person of interest in the case and the DNA that may have been Wall's may also belong to one of his male sons.
"It's possible that they could share the same genetic material with their father," she said. "Children do."
The line between homicide and suicide seemed as murky as the line between guilt and grief, according to family friend Andrea Brickey, who also testified Wednesday.
Brickey, who had known von Schwedler, Wall and their children for several years before von Schwedler's death, said she sat with Wall for more than an hour on the day after his ex-wife was found dead.
She said she was contacted by Wall's youngest son and immediately drove to their home. She found Wall face-down on his bed, wailing, she said.
"He said, 'Uta's dead. Uta's dead and ... the police think I did this,' " Brickey testified. "I said, 'Well, did you?' And he said, 'No, no. And if I did, I don't remember.' "
The interaction ended when she and another friend found Wall a bed at a psychiatric treatment center. She said the experience was "very odd" and she couldn't tell if Wall was grieving a loss or guilty of something worse.
Wall, who remains in custody in lieu of $1.5 million cash-only bail, has maintained his innocence from the get-go and is expected to plead not guilty if the case is ordered to move forward by 3rd District Judge Robin Reese.
The judge is expected to make his decision Thursday after both sides make closing arguments.
Von Schwedler was found dead in the bathtub of her Sugar House home on Sept. 27, 2011. She was an AIDS researcher at the University of Utah and a mother of four.