This is my very first critique here, and I hope everything is by the rules. I divided it into likes (where I will point out the things that I liked the most), dislikes and nitpicks (if you don't think they're necessary, just tell me, please). I hope that's okay.
So, here's my opinion on Miiztaylor's story.
Likes:
The idea -- I found it very original. It was such a nice way to stay true to the canon and to give us hope for Catherine and Warrick at the same time.
The ending -- I don't think it came too abruptly. They saw how Lindsey and everyone from the team coped with Catherine's death, and then she decided it was high time to move on. It was a natural thing to do. No big words were used, and that's what made it so beautiful. We can see that they are moving on together and that they are closer than ever, but you didn't make it mushy. Well done!
Moreover, Cath's stubbornness and her concern for Lindsey were very in character. I also liked the fact that Warrick was thinking about Eli so much.
"Another thing the job taught me: Nothing is surprising when it comes to what a human being is capable of." - This is so true.
Dislikes:
Okay, this is not really a dislike, not even close. It's just that I would repeat "It's been a rough couple of..." or put something similar right before "The sound of crying sprung me from...". In that way, you would link the event with Catherine to the beginning and make Warrick's thoughts about his job, Eli and Gedda a somewhat more separate -- but still integral -- part of the story. It's only a suggestion, of course.
I also have to mention the tense shifts from the first paragraph here. Warrick says, "In order to keep my mind off things I try and do what my friends have taught me over the decade I’ve worked with them. When you’re feeling like you screwed up, and that everything was your fault, think off all the ways it wasn’t. When you become disgusted..." And yet, the paragraph begins in the past, so he should say, "...I tried and did what my friends had taught me...". Then you switch to the present. I think that could be simply resolved by using different punctuation -- just put a colon after "them" and quote everything his friends had taught him.
Nitpicks:
First of all, I have to say that I am not the person you should come to for nitpicks -- I usually get so immersed in the story that I don't notice misplaced commas, split infinitives, typos and other subtleties. Also, I'm by no means perfect -- most of the errors I don't see because I make them, too. Anyway, this time (since this is a critique group) I made a conscious effort to catch little things. Here's what I found.
• "Years since I’d seen her; my family; my son." - I'm not sure that the use of semicolon is justified here since you're separating quite simple phrases. I think you wanted a longer pause, but I'd rather use commas nevertheless.
• "If one thing being a CSI taught me, it was to hold on to what I have." - The word order is a bit odd to me. I think that "If being a CSI taught me one thing..." sounds more natural.
• I think that it's "Undersheriff" or "Under-sheriff," not "Under Sheriff."
• "I hoped it would, but I couldn’t tare my eyes away." - It's a typo -- it should be "tear."
• "...which she tried desperately to blink away." - I just thought I'd mention this because some people claim that a split infinitive in fiction is a big no-no. However, since we all know how people use it all the time when they speak, and since the story is told in the first person, I wouldn't "correct" it.
• "'Catherine?' I asked gently as she sobs softened. - It's a typo -- it should be "her sobs".
• "'Rick?' Catherine ask and she looked up." - I think it should be "asked" so that the tense wouldn't shift. Also, I'd omit "she" or replace "and" with "as."
• "Her eyes hardened slightly, 'I can handle it.'" - "Slightly" should be followed by a period, not a comma because "harden" isn't a verb of speech. Anyway, I think this is just a typo as the rest of the dialogue is punctuated correctly (as far as I can see).
• "[O]n it's deserted grounds" should be "on its deserted grounds."
• "[A] view of Lindsey's school became visible" - I find this a bit redundant. I think that either "view" or "visible" would do, e.g. "Lindsey's school came into view." or something similar.
• "That left Greg, managing the nightshift." - I don't think you need the comma.
• "Something I’d never imagined." - I use sentence fragments a lot, but I would use a proper sentence here.
• "Whether or not to keep watching, or walk away." - It may be just me, but I somehow find the sentence a bit odd, somehow incomplete, the way it is. "Whether or not to keep watching; whether or not to walk away." and "Whether to keep watching or to walk away." would be my suggestions.
• "'Can we go?' she asked me, her inner strength had returned." - I think you should either replace the comma with a period or omit "had." The way it is now, you have two independent clauses separated by a comma only.
Miiztaylor, I truly hope you find something useful here.
TQ: Two days ago I found my very first fanfic. I didn't really know it was a fanfic when I wrote it -- I was ten and internetless at the time.
So, what was it about? One of my favorites characters from the show in question (I'll just say it was a teen drama

) died, and I was basically writing an AU/AT in which he would survive.
How was it? Even worse than some of my stories at fanfiction.net.

It was naive and full of dialogues which suited twelve-year-olds rather than high school juniors (or were they seniors?). Sentence structure and punctuation weren't so bad, though.

Actually, I think they were better than in my latest stories...
Edit: It's Lindsey, not Lindsay. Silly me.