I have no update to this in case it is of help to anyone else. It may be the solution user vdundzys had come across, I don't know.
Today I was tracing and I got the error message, a reshape line must only have one part in it. However I got it twice in succession, so I did the same tracing again and then zoomed in to see what was happening. See attached picture.
What is happening is that there are two vertices very close together but not along the same line I wish to trace. When I trace ArcMap is choosing to trace both of them. However it doesn't go from one directly to the other. As you can see in the attached image, there is a gap between the two.
It may be that the tracing line is doubling back on itself but I wouldn't have thought that would cause an error. Therefore it may simply be creating a spur line and then carrying on from the vertex the spur line came off, without actually going back to it before carrying on, if that makes sense.
Now the attachment shows I have really zoomed in to see this and you may be wondering why I have two points so close together. Well they are actually different data sets.
I am tracing off existing road data, which is a series of polygons. At the end of each road I trace, I need have it split from the road it joins. Although the roads are already split in the existing data, they do not follow the same convention I have to follow for the work I am doing, so sometimes I end up with points very close together. Hence the conditions for this error to occur then exist.
When I deleted the vertex that I did not require at the end of the spur line just now, I was able to finish the sketch without any errors.
What compounds the error badly, when it occurs, is the fact that ESRI have designed ArcMap so that after the error and any other sketch error occurs, the sketch disappears making it very heard to locate the cause of the error and it also makes one have to do the work again, which is most annoying. It may not seem like much but when your doing large amounts of digitising, the last thing you want is to have to repeat your steps because of such things. It's not as if the software is cheap.
Anyway I'm not sure what I would gain by taking this up with ESRI technical support but at least it is here in case it is of help to someone else.