Count the videos in a Youtube Playlist
05AB1E, 22 bytes
Assumes that the URL is passed without the https://.
Code:
.w’®Ã-ƒ¢’¡`&quot;&lt;li&gt;&quot;¡2è#¬

Uses the 05AB1E encoding. Cannot be tried online, because of internet access.
Explanation:
.w                       # Receive implicit input and read all data from the url
  ’®Ã-ƒ¢’¡               # Split on the string &quot;header-details&quot;
          `              # Flatten once which leaves the last element on top of the stack
           &quot;&lt;li&gt;&quot;¡       # Split on the string &quot;&lt;li&gt;&quot;
                  2è     # Get the third element
                    #    # Split on spaces
                     ¬   # Retrieve the first element 

This is what I get when running in the command line: