Looking at another WP site I do (which hasn’t been updated) it seems that the new 3.8.1 version is just ignoring single “carriage returns” in the published version that show up as paragraph breaks in the editing windows. (Neither editor was actually adding visible <p> or
tags :-\) The fix will just require doing two carriage returns instead of one. However, the same thing is happening with HTML code in a widget in the right panel. The published 3.8.1 version is not recognizing the <p> tag the same way as 3.8 did for some reason.
http://www.columbineuuchurch.org/cuuc/