How to switch various style sheets for different paths and pages, help needed, please advice

Hmm... I don't know much about theming, but have you double-checked the details?

Is your theme's name "drop" or you have changed the function's name accordingly?

For '/path-'. arg(0) .'.css', do you have style sheets named path-node.css or path-taxonomy.css or path-admin.css etc, to be loaded when you are viewing a node or a taxonomy list or an admin page, or whatever you want to style differently?

Or you might want to modify that concatenated style name, depending on what you want to style differently.

Other solutions to consider are
http://drupal.org/project/sections
http://drupal.org/project/taxonomy_theme

======= Edited to add:

Also check the produced html source in your browser, to see if the right style sheet is included or not, and which one is included in different cases.

What did you do to fix it? I've been trying to do the same thing, but to no avail. I can't get it to display anything in the header according to path.

I use Zen on Drupal 6 and there is no problem with my subtheme. I created it with Zenophile and I get mytheme_preprocess_page (commented) function at line 117 of template.php. I just wanted to include a path-first-alias-segment.css file if present; no path-front.css. My purpose is to everride some css rules based on path. Here is my function:

<?php
function mytheme_preprocess_page(&$vars, $hook) {
  $alias=drupal_get_path_alias($_GET['q']);
  $alias=explode('/',$alias);
  $path_style = path_to_theme() .'/path-'. $alias[0] .'.css';
  if(file_exists($path_style)){
       drupal_add_css($path_style,'theme','all',FALSE);
       $vars['styles']=drupal_get_css();
  }
}
?>

Two notes:

1. If you want to use filnames in the form path-node.css, you should change drupal_get_path_alias() function at line 3 with drupal_get_normal_path(), otherwise you are stick with aliased path (if you use path/pathauto module, you'll have /my-nice-node-title instead of /node/123. Here is the code:
   

   <?php
   function mytheme_preprocess_page(&$vars, $hook) {
     $alias=drupal_get_normal_path($_GET['q']); // <---------- here is the different call
     $alias=explode('/',$alias);
     $path_style = path_to_theme() .'/path-'. $alias[0] .'.css';
     if(file_exists($path_style)){
          drupal_add_css($path_style,'theme','all',FALSE);
          $vars['styles']=drupal_get_css();
     }
   }
   ?>
   

2. Double check you're calling the right CSS file using the dirty die() trick:
   

   <?php
   function mytheme_preprocess_page(&$vars, $hook) {
     $alias=drupal_get_normal_path($_GET['q']);
     $alias=explode('/',$alias);
     $path_style = path_to_theme() .'/path-'. $alias[0] .'.css';
     
     die($path_style); // <--------------- here is the awful trick. Please, don't tell my mom I use this! ;)
   
     if(file_exists($path_style)){
          drupal_add_css($path_style,'theme','all',FALSE);
          $vars['styles']=drupal_get_css();
     }
   }
   ?>
   

I had it up and running with no hassles.
Bye