I removed the toilet, as well as the heating vent, and finished removing all of the floor tile.  Removing the toilet was quite easy, although some water did get on the floor.  I also managed to crack the base of the tile trying to get the corroded bolts out.  Fortunately I was not planning on reusing the toilet, but I would suggest that if you are you should be very careful, as it cracked quite easily.  I was very happy to find that the mortar came off the floor cleanly, as I was not looking forward to having to replace the sub-floor.  You may notice that there are some gaps in the floor on the left side of the picture.   I had originally thought the they just did a crappy job laying the floor, but it turns out that these were conveniently labeled “Pipes” and were easily removed to check the piping beneath.