Likely the various documents belong to discernible categories such as client proposals, or memos, meeting minutes, etc. Within these categories there may be some sub-categories such as client proposals from 2004 through 2006.
Once you identify these "objects" or categories, you can then decide on naming conventions for all documents. For example:
A Client Proposal that was approved and completed by employee Jason Smith in 2004. With a shared network drive you may see a 4 Tier directory structure like this:
> Company Resources > Client Proposals > Jason Smith > Completed 2004
It seems like extra work, but the organizational value of such an approach is invaluable. For this to really work everybody will need to:
A) Know of the existence of this document solution strategy
B) Know how to access it properly
C) Understand exactly what work they do that needs to be managed in this way and when
D) Understand where the various documents they use go and how to determine which category the document goes into
E) Uses a standard naming convention
F) Everybody has access to written instructions for exactly how documents are to be named with complete, accurate examples.
From my above example we may determine all client proposal documents names start with a client id number, followed by the date in this format dd-mm-yy. If a status marker such as completed needed to be there then it could be assigned a common character like c, p for pending, cn for canceled etc.
A file may then be named like this using this running example: 4567-12-07-04-c.doc
When it a file is saved in the appropriate directory and named properly, it is very easy to find. Rather than search, you would browse a directory structure that you understood. In the worst case scenario, if it wasn't saved into the proper location, but was named correctly the search would be very easy to perform. If it wasn't named correctly, but saved into the correct directory, again searching would be easy.
These solutions work perfectly, but only if the people understand them, how to use them, and obey the required protocols for saving and naming of documents. Just an approach that jumped out at me.