This is very frustrating. I had this same problem with using the Joomla com_redirect and hoped that ReDJ would solve this problem.

I can put in a URL to redirect and that works fine. But if I put in a bogus entry such as domain.com/lalala it goes to the home page no matter what part of the website I'm on. Now, if I put in domain.com/validdirectory/lalala I get a 404 error. But that's if there is a valid directory and I just added the "lalala" to it.

I am using the htaccess.txt for my .htaccess that comes with Joomla 2.5. Here are my settings in ReDJ Community plug-in:
Status Enabled
Access Public

Basic Options:
Custom page 404 YES
Page 404 English (en-GB)
Track errors YES
Track referers YES
Referers to exclude {self} {none}
Redirect any error NO
Redirect URL (left blank)

Advanced Options are left blank.

I also did a Clear Cache and a Check In. Still can't this to redirect to 404 for bogus entries from the root path of the domain.

Thanks in advance for any help you can offer!

I am using a Shape5 template and their S5 Menu system. Does that answer your question?

You gave me an idea! I am using "Blank Component" for the home page. I disabled it and things worked much better, except "Blank Component" disabled broke the home page. "Blank Component" is used to allow you to create a Joomla page without an Article on it, just modules. I need further testing to confirm this is the problem but it looks promising. Thanks!