I just stumbled across this, and after reading your Authors Note, thought i'd review. An interesting start to the story, and I loved what you did with James/Lily and Sirius' fangirls.
Formatting - Your formatting needs some work, as there are large inconsistent spaces. Also, at one point, you used dashes/underscores to create your scene break, but at the two other points, you didn't. It's confusing for a reader and slightly messy, but easily fixed. :)
Punctuation and Grammar - A few things caught my eye here...
+ "finish this essay.” Remus said
This should be '"finish this essay," Remus said.' Note the comma as opposed to the full stop. This is because 'Remus said' is a dialogue tag and not an action. If it were '"finish this essay." Remus sighed' then it would have the full stop, as he didn't actually sigh it. Does that make sense? There is a really good thread on the forums that can explain it better than I ever could :P (Go to Writers Resources -> Grammar Guidelines -> Everything You Ever Wanted to Know About Dialogue. Grammar and Parts of Speech should be helpful for this as well)
Characterisation - As I said before, we don't get to see much of who Jane is, as she doesn't get much of an introduction, other than she is Lily's best friend. Be careful here, as this is quite cliche in Sirius/OC and Remus/OC fics. I'm not saying it is, as I feel even from this, that the plot could be quite good, i'm just saying be careful. I'm interested to see how you might work around it. :)
Sentence Structure - This might fall under punctuation and grammar, but 'beside her, her best friend Lily Evans' really bugged me. 'Her' was written twice, immediately next to each other, which I didn't feel was needed. Also, on sentence structure, I feel commas could have been used a bit more to help the paragraphs flow. Eg. 'and passed it to Sirius. Sirius copied it down and leaned back in his chair.' Here, it could be, "passed it to Sirius, who copied it down and leaned back in his chair." Not only does it stop you from repeating words over and over again, but it creates more of a relaxed tone, which is what your looking for in this scene. That said, in other parts, you went comma crazy! Haha, it's all about finding balance; I know from experience. :S
Pacing and flow - The flow was disrupted by the larges spaces and sentence structure, but other than that, was alright. The pacing however, was a bit off for me. I found it jumped a lot and moved very quickly for such a short chapter. There were a couple of minor things, such as when you change the POV of a character (you start pretty much in Remus' then changer to Sirius' within the same space at the start) then you swap to Jane's and it comes across as slightly confusing at first, but then you get used to it. Last scene, you start the paragraph in well, not present tense as it's from 3rd person, but you know what I mean, and then suddenly it's memories/really past tense. I didn't know what was going on, thinking that the past tense was what he was doing at that moment, but then you swap back to what he was currently doing, and I was very confused :S The dream was a nice touch though. ;) Good job on that one.
Anyway, enough of my ramble-y, spontaneous review. Hope I helped a little, and that you keep up the writing.
Good job, Adele.
Author's Response: Hi, thanks so much for taking the time to review!
I didn't notice that one of those lines was a bunch of underscores, I don't know how that happened, but I'll fix that up right away.
You've kind of lost me with the punctuation and grammar stuff, lol. I'll have a look at thread on the forums, because I'm certainly aware that I have lousy grammar, but I've never quite known how to fix it.
In my head I actually have a very good idea of who Jane, and I'm trying very hard to keep her out of that whole world of cliche Mary-Sues.
It's evident from this review that I'll need to go back and do a lot of editing. These sentences are quite awfully written.
Yeah, I'm also very aware about the pacing and flow. The quick changes of POV bother me too. I'll see if I can make all of that easier to understand. It's the same with the memory which, I agree, was rather messily done.
I'll have to do a big overhaul and fix up you problems you've mentioned. Thanks so much for the review. It's been a big help :)