It is of course never wrong to use the title of the person to whom you write. In general I think it is fine to use Dr. since that is the degree most have. This may not work so well in cultures where titles are more of an obsession or where hierarchy is still well established. If the person writing is a professor, then you are of course writing from the top position and so you will either direct letters to someone at the same level or lower. This simplifies things compared to if you, yourself were not at the professor level.
As an editor of a journal I often use the term Colleague instead of Dr. this or Professor that. This is because the tile may not be completely obvious from the manuscript and I do not permit myself time to Google every author to find out. Since I am also a professor, it feels relatively safe to call everyone a colleague.
To sign off I often use my first name except if the mail has some formal aspect where, if it was a letter, I would have used my full name. In all my e-mail correspondence, I have found almost without exception, that once I sign with my first name, the mail reply will inevitably greet me by first name and be signed by a first name. I try to be a little sensitive about it but not overly so; I have "my" culture, the person I correspond with his or hers and none is above the other in my view. So In any correspondence I will open the first mail with Dear Colleague or Dear Dr. So-and-so. If the response is signed by first name then: titles away. Otherwise I will countersign correspondence with first name to break the ice.
It seems e-mail is often more forgiving than regular letters or traditional contacts. I think internet has an informal context which implicitly signals to everyone that it is less formal. I have not seen research on this but I can see, for example how students can ask quite blunt questions over e-mail while almost trembling and excusing themselves when standing at my office door (not that I am in any way trying to be intimidating).