Just to be clear, operating systems are not "per say" case sensitive, but rather the file systems.

Regarding your question, I personally would recommended renaming files/paths to be lower case and replace spaces with underscores, but thats just me. If you have a lot of files and references to those files in your website, a couple liner script would definitely help.

You could always give the Apache module mod_speling a try. I have never used it but according the docs it looks like what you are looking for.

Requests to documents sometimes cannot be served by the core apache server 
because the request was misspelled or miscapitalized. This module addresses 
this problem by trying to find a matching document, even after all other modules
gave up. It does its work by comparing each document name in the requested 
directory against the requested document name without regard to case, and 
allowing up to one misspelling (character insertion / omission / transposition 
or wrong character). A list is built with all document names which were matched
using this strategy.

You can enable it like this:

a2enmod speling

Hope this helps.