Guys guys I have two more snippets nearly done (just need to get them back from my beta-reader and make edits)!Yeah you've never heard that one before.

It's a hot day in winter when I can tolerate a holy knight more than a mage.
I appreciate the sentiment here, and it's a great line to start this thing out, but the bolded part could be... bolder. More expressive. As "Noir" is really more of a film descriptor, what you're generally going for in writing this genre is generally closer to straight Hard-Boiled: unforgiving descriptions and gritty, violent imagery.

Same old routine as always.
This is your second "as always" in just a few lines. There's no need for it here.

I reached into my coat pocket. Miho drew a sword and put it to my neck from behind me. I let her take the coin pouch and toss it to Marla. The blade was removed and sheathed. I checked my pockets to make sure Miho didn't take anything else. She didn't.
I like this scene, and the casual attitude Horst describes it with. It would come off a little better, I think, if he didn't explicitly give every detail:
Quote Originally Posted by me
I reached into my coat pocket, felt the tip of Miho's sword jump to my throat. I held still as she took the coin pouch and tossed it to Marla. When she removed the blade, I checked my pockets to make sure she didn't take anything else. She didn't.
It turned out my client's husband wasn't the only one missing. Marla had lost three girls in the past month after paying a visit to the priests at the temple. I knew Marla was telling the truth. She's always had a rule with her girls that they could leave whenever they wanted to as long as they told her first. Marla was worried about them.
Marla, Marla, Marla! There are no other actors in this paragraph, so there's no need to repeat her name; it's clear enough. Perfect opportunity for some descriptive, probably derogatory--or at least a bit offensive--identifiers. There's a reason people associate noir fiction with the narrative referring to a woman as "the dame" (etc) rather than by name.

Idiot. I left without another word. I had told Marla that I would try to find her girls, and I was a man of my word. I didn't give my word lightly.
One nice thing about noir is there's a bit of freedom-of-tense that comes with the genre. The main character/narrator is allowed to talk to the audience a bit, so you can make this a little smoother by putting the last sentence in present tense. "I don't give my word lightly" is much more confident.

I knew that if I could not drop him in a single shot with my crossbow he would call for help. I knew my hand crossbow did not carry enough power to stop him.
The bolded part above is redundant/awkward. You clarify what exactly you're shooting with in the next sentence. Keep the narrative crisp and terse; you're the narrator; you've got places to be.

Beautiful, deadly Miho.
This is a great line, but it doesn't belong all by itself like this in noir fiction. Attach it to the previous paragraph or give it some more description; what Miho does, how she looks, if she says anything, all that kind of stuff.

I hope you continue this; it's a lot of fun to read! Generally, the things I would say to work on style-wise are:
As the narrator, when in doubt...
...make yourself look slick.
...disrespect everyone else off-hand.
...describe the violence point-blank.