Yeah, seems a bit implausible that he would have got out of bed, gone to the window, put on his legs and picked up his gun without taking notice that she wasn't in bed. I'd also add that it has now been revealed that it in an en-suite bathroom with nowhere to go, so why would an intruder be in there, behind a closed door?
In the case of his defence though, their argument that it was a mistake and that he thought it was an intruder is all they can rely on, whether its true or not.
He is clearly guilty of killing her, the only way they can prove it was deliberate murder is whether there is any truth from other residents that an argument was going on beforehand. I'm sure forensic evidence and details about the bullets and how they were fired may later reveal information.
At this stage though, it would look from an observers perspective that its going to be difficult to prosecute that it was pre-mediated murder.