I have JAA, CAA and FAA licences, and one logbook - neither FAA nor CAA have ever had a problem with this. I struggle to see why there's a reason to copy an FAA logbook into a JAA logbook - they all contain substantially the same information; if you really want to switch, just transfer the totals over then start from the next line.
But, I have always filled in my own logbook, with a line per flight, not per day. The practice of an instructor filling in a student's logbook for them strikes me as highly irregular - multiple airfields on one line is also rather odd but should be okay so long as the total flying hours are correct.
G