Edit 1: Banality

[Richard]

Hey Cat,
There are parts of this poem that I quite like. However, there are some dubious word choices here and there in the poem. I'll go into more detail below:

Through streets littered with 
tin cans and chit-chat, -I can't say I've seen too many tin cans rolling around the streets in the cities I frequent, but may be this is true in other cities I've never visited.
I’m making my way home
on a mellow Tuesday evening. -I understand why you used the word "mellow," but I can't help but wonder if there is a more effective word you could use here. To me, a word like "mundane" might be more consistent with the tone of this poem.
While I wait for a train
that goes my direction, -I like how the wording here makes the train even sound banal.
I decide to add to the mess -I find that this and the next line gave me the impression that the speaker feels a bit defeated.
by lighting up a cigarette.
I inhale deeply as -I don't think this line is necessary. What else are you going to do with a cigarette other then inhale it? I would also suggest adding a line later in the poem describing the speaker throwing the cigarette butt on the ground. I think if it's done right, it could be a potent image.
my lips kiss the bud; -I like this line because it leads nicely up the coming simile.
stale smoke numbing my throat
a feeling like that of a sore love-story. -I would drop "a feeling" from this line. I love this simile. It works well with your tone in this poem.
Moments pass by like pedestrians -Another nice simile. It's consistent with the imagery of the poem so far.
when I spot a faint rumble -Do you mean "hear" instead of "spot", or are you mixing up the sense intentionally to create emphasis?
coming from a near distance;
Pa-dum-dum, Pa-dum-dum, Pa-dum-dum -I like the use of onomatopoeia here. The sound of the train is a wonder image for describe the mundane nature of daily life.
 
It’s that distinct sound -Is it really distinct if the speaker takes the train home every day? May be he/she doesn't, but I suggest using a different word here other than "distinct".
of going home,
presented by a carriage
that is marked with graffiti -You have a chance here to deliver a powerful image if you describe the graffiti more.
and the occasional spot of rust.
It slowly grinds to a halt
with a loud screech and a whir. -This image appeals the reader's sense of hearing.
Its gates squeak open -This image also appeals to the reader's sense of hearing. My question is how can you describe these sounds so they seem more banal?
and out steps its guard.
He dons that unmistakable -I'm not a fan of the word "dons" in this line. It just sounds like a really old-fashion word to me. 
silly hat and uniform, -Why is it silly? I feel like you could explore this image more.
colored black and blue respectively.
He asks for my destination,
to which I softly reply; -Why does the speaker reply softly? He/she thinks the person is silly, so I wouldn't expect them to speak softly to him.
“Home, Sir, to Nessingway station".
I show him my ticket
to which he approvingly nods. -This line feels a bit unneeded. This is just a thought, but would it be more interesting if the guard sensed the speaker's disrespect and nodded disapprovingly?
I crack an awkward smile -If you used my suggest from above, then the awkward smile would be warranted.
while I step inside.
My eye catches a vacant seat -I get what you were trying to do here with the wording. However, this line created a pretty surreal image in my mind.
through the cluttered crowd; -This is more food for thought than a critique point. You already compare time to pedestrians earlier in the poem, so how could you compare this crowd to time? 
A rugged leather couch with
a piece of fabric tearing out. -I feel like you need to add a simile or metaphor here.
I sit down and rest my head
against the glass, staring through.
As the train slowly starts moving,
making that ubiquitous hum:
Pad-dum-dum, Pa-dum-dum, Pa-dum-dum -I find this whole stanza serves an important purpose to get the speaker on the train and moving. However, this stanza feels more like prose than poetry in spots. This is something I'm often guilty of myself, so I feel your pain here. I would suggest reworking this entire stanza with the focus of trying to add more figurative language to it. 
 
Through the stained windows
I spot my vague reflection. -I love how the speaker views his/her reflection as vague. It works well with the idea of banality.
Together we see the sunset -This is a nice line because it actually emphasizes the speaker's loneliness.
accompanied by an ever-changing décor.
As if the credits from the end
 of a movie roll through
with a clichéd title like:
“Another day", starring myself -I like this metaphor of the ending day being like the end of a movie. I would actually suggest expanding it a bit. May be have the speaker mentally revisit the train station and the guard to include them some how within it.
while the rails take me
to the end of my destination. -I would drop this and previous line because it doesn't go with the movie metaphor.
Instead of the screen turning black,
I get up and step outside, -I wonder if you could change the time in the poem slightly and some how connect the night greeting the speaker outside the train to the black screen in the movie metaphor? Just a thought.
spotting my reflection in the glass
one final time, while saying under my breath:
“Goodbye and until tomorrow” -I would suggest having the speaker wave to his/her reflection because then it could wave back. I just think that would be an interesting image to explore.
The train slowly drifts off
yonder towards a setting sun, -This line would have to change if you take my suggestion above about the night.
bidding me farewell with that distinct sound:
Pa-dum-dum, Pa-dum-dum, Pa-dum-dum -I like the repetition of these lines. As I said above, this sound works well with the poem's tone.

I think you have a great first draft here. I would suggest spending most of your editing efforts on the second stanza and expanding the movie metaphor. I look forward to seeing where you go from here.

Cheers,
Richard