Investigators also went into Pistorius' home without wearing protective foot covers to prevent contamination of the crime scene, Roux said. Botha conceded that was true and said it was because police didn't have any more of the covers left.
Roux questioned police arguments that a witness heard sounds of an argument before the shooting. The witness, Roux said, lives 600 meters (more than a third of a mile) from Pistorius' home. Prosecutor Gerrie Nel countered that the witness lives 300 meters away.
Would he run?
Botha told Magistrate Desmond Nair that investigators believe Pistorius is violent and might flee if released from jail.
He described two encounters with Pistorius, one in which Botha said the track star asked someone else to take the blame when a gun went off at a Johannesburg restaurant.
Police said the second incident took place at a racetrack, where Pistorius allegedly threatened to assault someone.
Authorities have also said they have responded to previous domestic incidents at Pistorius' home, but have not elaborated.
In his statement Tuesday, Pistorius said he and Steenkamp were deeply in love and said he was "mortified" over her death.
Defense attorneys are trying to overcome South African law, which makes it difficult for defendants accused of premeditated murder to get out on bail. The law requires evidence of "exceptional circumstances" to justify release.
Nair upgraded the charge against Pistorius to premeditated murder Tuesday, saying he could not rule out the possibility that the track star planned Steenkamp's death. But Nair said he would consider downgrading the charge later.
In a statement read by his lawyer Tuesday, Pistorius said he would not try to flee or influence any witnesses if he is allowed out on bail, and he said his release wouldn't be a danger to public order.
Case rivets fans and friends alike
The case of the global sports hero known as the "Blade Runner" has riveted stunned fans around the world.
Social media reaction to the case appeared to come down against the sports star but was still noticeably mixed on CNN's Facebook page.
"There's no amount of tears that will save you," said Anthonia Nneka Nwabueze. "Pistorius must face the law for brutally killing an innocent girl -- Reeva."
"My favorite athlete but what he did is grave and must be punished," Carlos Alvarez Ochoa said.
But another person who posted called for patience.
"(N)one of us were in the house when his girlfriend was murdered, let's hold off on casting stones at Oscar Pistorius," said Adrian van Liere Since. "Just like anyone else, he deserves a just trial, and in my eyes remains innocent until proven guilty."
Coming to his defense were two acquaintances.
"I've never seen him show an angry side. I've never seen him lose his temper," Vanessa Haywood, a model and longtime friend, told CNN. "He's an incredibly kind and gentle human being."
Another endorsement came from a former girlfriend.
"I would just like to say, I have dated Oscar on off for 5 YEARS," Jenna Edkins said on Twitter. "NOT ONCE has he EVER lifted a finger to me, made me fear for my life."
In an interview for Wednesday's "Anderson Cooper 360," Adam Steenkamp told Jake Tapper "there was no indication that anything was bad. I mean, we know Reeva. We knew Reeva. She was happy. And if Reeva was happy, everything was OK... and everything was good, then everything was normal."
Steenkamp said he never spoke to his half-sister about Pistorius, and she didn't discuss the relationship much -- if at all -- with anyone in the family. So, without any in-depth knowledge, his family keeps vacillating about what the evidence suggests happened, he said.