Yes, you should have a real 404 page.
- You'll help the people that follow their links - you should have a list of links that they might be looking for - and a search box. Remember, you want these visitors to stay on your site, not bounce.
- Google wants you to have one. In fact many bots will test your site has a 404 page that returns the correct status (404 of course). Make sure you test yours. Many incorrectly return 200 (ok) status.
If you want to keep (some of) the linkjuice, and you know where they want to go, you would 301 redirect to the correct destination.