One of my clients web pages has a error in the theme which calls a redundant .css file that does not exist. The page however, looks fine. Thus the client is not willing to have the error fixed. What reasons can be given for fixing the error when it does not cause any issues with the page display.
Http calls have the biggest single impact on front end performance, reducing them should be a priority for every webmaster (even just that one little one that's 404'ing).
From Yahoo's performance guidelines:-
80% of the end-user response time is spent on the front-end. Most of this time is tied up in downloading all the components in the page: images, stylesheets, scripts, Flash, etc. Reducing the number of components in turn reduces the number of HTTP requests required to render the page. This is the key to faster pages.
If you can't fix it, at least put a blank CSS file in the right place so you don't waste time with 404's for it.
In regards to the mega SEO engine that is Google....
Basically, no. It does not hurt anything, including your SEO priority.
You could argue that it wastes a few milliseconds generating that 404....