It is always a very good practice to start testing as early as possible.

By not fully implemented if you mean still under development, then I suppose that is not such a great idea. Yes, you can go for incremental build releases for testing, that might be helpful.

When you say that your testers all log the same bugs, well there's your problem! Do you maintain a central repository for tracking bugs? a bug tracking system of some sort? If yes, then do your testers check whether a bug has already been logged before they log their list of bugs? Do they not coordinate among themselves? There seems to be a serious communication and understanding issue.

It is always a very good practice to start testing as early as possible.

By not fully implemented if you mean still under development, then I suppose that is not such a great idea. Yes, you can go for incremental build releases for testing, that might be helpful.

When you say that your testers all log the same bugs, well there's your problem! 

Do you maintain a central repository for tracking bugs?

A bug tracking system of some sort? If yes, then do your testers check whether a bug has already been logged before they log their list of bugs? 

Do they not coordinate among themselves? 

There seems to be a serious communication and understanding issue.