@Aleksi "Lex" Kilpinen: Let's say I've got 400 pages of attachments (I think the default was 15 or 20 attachments per page), all of them small files, not more than a few hundred KB. So, I need to find a particular attachment in those 400 pages and delete it so I could upload a new one (or just delete it). Let's say this file was uploaded 3 years ago. So, the simplest way would be to sort attachments by date and go back 3 years. The problem is, I don't know on what page the 3rd year backwards begins. I could make a rough estimate based on browsing a few pages, but I really have no idea on what page that particular attachment is.
On the other hand, from the topic I'm currently browsing, I could just copy/paste the name of the file in a search field, the search would return the exact file that I need, I'd delete it from the server (attachments directory), upload a new one (or not) and voila, job done

.
As I said, the previous function (a link to the file in the "Attachments and Avatars" admin section) would be even better, but I think the Search function would be easier to implement

.
EDIT: Or, there could be a link right next to the attachment in the post (that will be shown only if you try to edit the post) that will read "Search in attachments" that will automatically invoke a search function in the Attachments and Avatars section (previously implemented), like in the picture below.
@shawnb61: Yeah, that would also be a nice function (type of extension, info, hash, etc.), but what I'm currently looking for is a simple "Search through attachments" function.
Just to make things clearer, here's my Attachments and Avatars section.

423 pages of attachments and I have to find a single attachment in those 423 pages and delete it

. Let's say I have to do this on a daily basis. It takes me an average of 5 minutes to find the attachment.
I also think that this should be implemented as a core function in 2.1. It shouldn't be too hard to implement, I guess most of the code could be taken from the regular search function and just adapted

.