Morning light attacks through a tear in the curtains.
attacks who?
"...the ****?"
Time to wake up.
"Oh."
Not sure this inner monologue was necessary.
Tuesday. Anything but Tuesday. At least Mondays you can hate. People will know what you mean. Tuesdays just
are.
Hey, I like this!
To its credit, this Tuesday will be different from the last. Because today, he's going on a date.
Not sure about the jump to future tense in the first sentence - IMO it's better to try and stick to one tense as much as possible.
"Going" is actually a lie. [color=orange]Who's POV is this from? Who's the narrator telling the story? So far it reads like 3rd person omniscient that sometimes lapses into 3rd person limited - I'd recommend sticking with one or the other[/spoiler] She's coming over, they always do.
At "they always do", I was starting to guess that the MC's a serial killer. Speaking of going, he never really does. The way he stays put without any help would probably be impossible outside the internet age.
I had to read twice before getting what you mean. Suggest rephrasing "The way he stays put."
He opens a cupboard, only to find an empty jar of instant coffee. He was bound to run out, he knew he would, it's just he pushed it off his mind. "Why call it instant, anyway? You're still expected to make it..." he asks himself, pretending to relay the question to whoever decided on the name.
At this point, nothing had yet happened. A guy woke up, and is waiting for his date in his flat... And that's about it.
Sitting on the couch with a cup of hot water, he switches on the TV and skims through his favorited channels. All subscription, mostly porn, and mostly not showing anything at this hour.
At what hour? I had so far assumed it was about 7 or 8 AM (since you've mentioned it's morning previous), with the MC having woken up from sun rays shining on his face... He stops at BBC America.
"The Surrey Slaughterman' as dubbed by media still unidentified, says police. Latest victim attributed to the same killer is Crystal Mgawi, discovered by a neighbour who chooses
chose (should be past tense, this all ready happened to remain anonymous.
"A neighbor who choose to be anonymous" sounds a little bit strange. Did she have that many neighbors? If the person who's discovered the corpse chose to stay anonymous, why would the police say that he's actually her neighbor? Why mention this at all? Her death seems a repeat of previous 'Slaughterman' crimes, from the lack of an eyewitness to the accurate adherence to slaughterhouse procedure..."
What's slaughterhouse procedure?
"What a sick ****!" he thinks while lazily toying with the curls of his blond, medium-length hair.
Is his hair important to the story? If this is 3rd person limited, then he would never care to remember that he, in fact, has "blond, medium-length hair," and if it's 3rd person omniscient, I think that it can be relayed earlier in the story. I would use something like, "He wondered if his new date would appreciate the effort he's put into taking care of his hair.
Doorbell. He's dozed off at some point. It is midday, his pyjamas are damp and an empty cup lies at his feet. She's at the door. "Coming!" he yells while changing into a pair of black jeans and a white t-shirt.
He either changes really fast, or yells really slowly... 
"Just like chess!" he notes, reminding himself of an impeccable fashion sense and a perceivably sharp wit.
He thinks black jeans and a white shirt are great fashion items? Is he being ironical while having an inner dialog with... himself?
"Hi you...you!"
She was beautiful. And never heard from again.
IMO, last line could've been stronger. I guess my biggest problem with it is, again, a jump-in-time. If we all ready know that she'll be killed (because the narrator tells us), that means that the story's isn't just in present tense.
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So I wrote this today. Would like to see some feedback, I guess, especially if you're Gebohq. Also, it's not interactive...