A good introduction to the classic dystopian environment. Three stars for potential. However, I found several sentences in the first paragraph to be awkward.
The initial sentence is a bit of a run-on and doesn’t clarify itself quickly. I think the segment from the first comma to the second comma could be eliminated, and instead a synonymous adjective be attached to the “glances of strangers” phrase. This would improve flow and coherency.

For the second sentence, I understand what you’re attempting structurally, but a less hypothetically worded approach would be more beneficial. Here are some options for how that could sound.

“After a visit to the ladies room, she was perfected enough to walk into the office and smile at the receptionist.”

or

“After a perfection-restoring visit to the ladies room, she walked into the office and smiled at the receptionist.”

Something along those lines.

The third sentence just needs minor revision. For clarity’s sake you could combine “took a seat” with “as directed”, making it

“She was directed to a seat in the room beyond, but she didn’t have to wait long.”

Alternately, you could keep what you have and, with a minor additions, re-arrange it into two sentences.

“As directed, she took a seat in the room beyond. However, she didn’t have long to wait.”

In the second sentence of the second paragraph, you need to replace “then” with “and.” “Then” is implied in the verb “examined.”
Also, the existing sentence structure states that he looks at the documents before looking at himself. You need a word to place the papers in a location relative to him. For example,

“He sat across from her after a firm handshake and examined the papers that lay before him.”

Which could easily be switched with

“…the papers on the table.”

or any number of phrases.
Lastly, don’t be afraid to format your piece so that the direct quotes are more visually noticeable. It encourages the pacing of the story and makes it engaging for the reader.

I know I’ve focused heavily on the grammar elements, but the quality of writing can make or break a story. Always remember: If concept/story is the “what”, the writing is the “how”.
In many ways, good writing can make even the most mundane thing interesting. Seeing as this story’s concept is quite intriguing, all you need is to refine your prose and this could be very good indeed.

Ambrosia, your line about the hairspray is great, a perfect visual in only a few words.

Memento, you are being very critical, five comments is too many, this is not an editing site. Consider combining all of your suggestions into one precise constructive comment and delete the rest.

If the structure is closely inspected, it changes drastically once she starts speaking and is perfectly fine after that.

Also, this is futuristic, language could simply be different then; sci-fi writers do it all the time.

Could it be that the lines before that have to do with her personality, a glitch maybe? Maybe she’s a droid. If you see odd structuring or phrasing, work with it, make it a new truth.

Forgive me if I seem heavy handed or abrasive. I seek only to engage in supportive critique so as to encourage the author.

Awesome beginning! Memento has some nice points, but in the end, you are the author and can choose your sentence structure to fit your genre. I myself had to read the first sentence twice, but the glances of the strangers is necessary to the scene and I say you should keep it. :)

Thank you all for the feedback, I appreciate the acknowledgement and confirmation that someone has chosen to read this smeared stream of consciousness.

I apologise if grammatical errors distracted from the communication of the idea itself: I often find I have to condense myself after the fact and do an inelegant job of it.