Well, if you're looking at my avatar right now, then you can probably deduce that I'm a big fan of the Eradicator. He's one of my favorite characters in the Superman mythos and was, IMO, by far the coolest of the "Four Superman." However, upon a recent re-viewing of Superman Returns, I began to think that involving the Eradicator in a sequel may be problematic, and here's why.
My biggest complaint about Superman Returns wasn't the costume, the Donner influence, or the kid. It was the fact that Superman simply wasn't given enough to do. I felt like we, at best, only got to know him as much as the other characters, when we should have gotten to know him MORE than any other character, in particular the other heroes of the story (Lois, Richard, Jason, etc). Now, if the Eradicator shows up and the story follows a similar pattern to the one in the comics, he'll redeem himself somewhere along the way and become something of a hero. If this happens, he will no doubt steal the show from Superman. And even if Routh himself plays both roles, that still doesn't change the fact that a movie about Superman should actually be ABOUT Superman.
If the Eradicator is used strictly as a villain, I see some problems there as well. I think one of the things that makes the character interesting is that it began as a weapon whose purpose was to preserve Kryptonian culture and obliterate anything that would comprimise that, yet once Kal-El died, its motivations changed and it attempted to carry on his legacy as a hero. This sets the Eradicator apart from your typical Terminator-type killing machine. But if he's made out to be a flat-out villain, chances are we'll get the E-1000. Just food for thought.