It depends on why the 404 errors are coming up but in general terms, yes, high numbers of 404 errors can count against the quality metrics of your site and hurt your rankings.
Whenever Google spiders the web, they are following links from external sites to yours, your own internal structure, and your past indexed pages. While 404s themselves are not a negative indicator according to the linked article above, 404s of expected content due to errors in your internal linking or server configuration (i.e., a bad redirect rule) will lower the number of documents you have indexed and that is the "penalty" applied.
There are several things you can do to mitigate the effect of 404 errors:
- Use a custom 404 error page to suggest alternative navigation. The inbound user or robot should be presented links and a menu to assist them in finding other content on your site. Never leave a default 404 server-generated error page in place
- If the 404s are caused from external links, use 301 redirects to get the inbounds to the desired location
- Use an XML sitemap to tell search engines what exists. This helps to drop dead pages out of their indexes
Follow those simple steps and any penalty caused by excessive 404 errors should fall away over time.