Yes, please. That would be helpful. Thank's.
Should diagrams have colored animation like games?

Erik, I think that is overkill, not needed.
But if it is not more work for you guys, yeah, may look good...

Yes
I also would like another thing: 3D boards. Up to now the pieces have been 3D but the board has always remained 2D. I would like both pieces and the board to be 3D.

Yeah I think that's good. Is there a way to analyze with someone (set up a board with positions/load pgns for training?

I don't think you should add it automatically to every diagram, but you could make it an option in the "Design" box.
ADK

At playchess.com there is something called spy which allows you to view what's being threatened. It doesn't work however if you are playing another human (works with computer games)

It should be a choice (like in the part where you choose what pieces to use, board size co-ordinates) One thing I think would be helpful would be to have co-ordinates ticked on as a default (with the choice to, 'un-tick'). A lot of articles and game analysis have many notation references and with a lot of them having no co-ordinates on the board it takes that extra bit longer to read
(sorry for nitpicking at something that is already very good)

I do not think that it is necessary. When I play OTB the board does not light up. I prefer not to have this option. Please make it an option, if at all.

I think it should have that color. That would help other specially those who low rated have no idea. But it should be an option though.

Optional, yes, But optional for who? The poster of the diagram, or the user replaying the game? At the moment, options seem to be for the poster.

I think that there are a few situations where it would actually be problematic so it would need to be optional.
Retrograde puzzles are an example, and one situation in particular I can think of is a puzzle where an en passant capture is the solution (as the previous move needs to be made in the editor in order to enable the capture), but where the solver is required to figure this out on their own (via retrograde analysis). Showing the last move would give the puzzle away:
http://www.chess.com/forum/view/more-puzzles/mate-in-one2
Right now when you step through a game there is no animation. Should we change that and add yellow highlighting to the source and destination squares?