I noticed something which I think is interesting.
Even we all know that redirecting 404 errors to home page (or another page) isn't the right thing to do.
I was researching for a very popular keyword (non-English) for the keyword widgets (one of the most famous keywords), and I found that 8 of the top 10 results, for websites that 301 redirect 404 errors to home page or another section of the website.
I tried same for same keyword in English, and I found some (less percentage) are doing same also!.
Looks like the link juice effect of those 404 error pages, is stronger than the negative impact of redirecting 404 pages!
I know this may be with no effect (just a coincidence), but its also an interesting thing to research further!
Maybe others can check for keywords they are following and see if they notice same trend.