Are there any grammar or stylistic errors in my writing sample below?
Thump. Thump. Thump. This time, my eyes flew open, and I immediately looked over the side of the bed. Casey was gone again. A ghost. My mind flew through the logistics of there being an actual ghost in my apartment. Thump. Thump. Thump. There it was again, but just as soon as it came, it was gone. I once more got out of bed and climbed down the stairs, but this time I tiptoed. I was as quiet as a ghost, ironically. I was so quiet that a pin dropped could be heard. When I reached the bottom, I felt my heart in my throat. I just had to switch on the lights. Taking a deep breath, I slammed on the lights to catch the culprit, Casey. I found her head buried in the trashcan, searching for the steak bones I had thrown out at dinner. She had tried to sneak out while I was asleep to sneak a late night snack. The first time, my loud movements had scared her so in her desperate escape, she ran to the closet to hide. This time, she was unable to hear me coming. I smiled and patted her on the head and she sheepishly looked at me.
Ironically, your original question should have read "Are there any stylistic errors..." rather than "Is there any stylistic errors." If you want to check yourself, make the question into a statement: There IS stylistic errors doesn't make sense because "errors" is plural, as your verb should reflect.
...usually defined by the writer’s choice of words, figures of speech, devices, and the shaping of the sentences and paragraphs.
The rules of creative writing are often few and far between, but it is important to note how much latitude your instructor will allow.
Casey was gone again. A ghost.
These two statements are confusing. How does the fact that Casey is gone connect to a ghost? Additionally, the first sentence is complete. The second is a fragment. Clarifying how Casey and the ghost are connected might take care of this. The following creates two complete thoughts and clarification: Casey was gone again: had he heard the ghost? (They could also be two separate sentences.)
Next, steer clear of "logistics."
This is an awkward sentence. "Logistics" is a word that doesn't fit with a condition as much as with arrangements: something that has been organized. It is defined as:
...the branch of military science and operations dealing with the procurement, supply, and maintenance of equipment...
Ghosts deal with nothing that is contrived or organized if we believe in the existence of the paranormal. I might go with something that seems a natural reaction.
My mind raced as I tried to comprehend the possibility of a ghost in my apartment!
Then, look at the line about being as quiet as a ghost—it's too contrived for my taste. If you turn it into a private joke in your own mind, it might work:
I was a quiet as...I chuckled nervously to myself...a ghost.
However, I question the veracity of the statement. Isn't the thumping (the noise) evidence of a ghost? If so, I might say:
I tiptoed down the stairs, trying to be at least quieter than what seemed to be a noisy ghost waking me from my sleep.
Leave out the "pin...drop" cliché. You have already talked about being quiet in context of a ghost. The reader has gotten that idea. Another comparison is redundant at the least, if not overkill.
Heart in the throat is also a cliché, but I feel that it is a realistic reaction, which makes your character believable. I might write...
I couldn't swallow: it felt like something was lodged in my throat...maybe it was my pounding heart.
I wouldn't "slam" lights. How about smacked or frantically fumbled— your heart is pounding in fear.
You turn on the lights to catch the culprit. I would stop there. Then I would write:
There was Casey, head buried in the trashcan, chomping on steak bones left over from my dinner.
The next sentence uses "sneak" twice. Try to find another for one "sneak."
Your surprise for the reader is very good, but your closing loses the energy you have nicely created up till now. Note that she hadn't heard you coming and was frozen in surprise upon being discovered. Let her sheepishly hang her head, while you ruffle her ears and promise yourself to put the trash out next time before you go to bed. If you say she had hidden in the closet the first time, it invalidates your scenario of a possible ghost and any reason for your fear. Stick with a spontaneous reaction that fits with the story's energetic pace.