A dotted line sounds like you are creating paragraph text. Is Convert to Artistic Text (control-F8) shown on the text menu?
With the text object selected, try pressing control-F8 anyway, and maybe try pressing it a second time. One or other should remove the dotted line.
OK, that's a better description. We usually call those handles.
As you probably know, you can change the size of part of a text object (by selecting some of the characters) to make them a different size to the text object itself. Sometimes though you can end up with all the characters (or sometimes, all of the characters other than a space) being a different size to the text object, which can be quite misleading.
This should fix it ...
This should also set the same size to each of the characters and I think will clear your problem.