Although you've said you've used a single Z
in the format pattern, this works:
DateTimeFormatter format =
DateTimeFormat.forPattern("EEE, dd MMM yyyy HH:mm:ss Z").withLocale(Locale.ENGLISH);
DateTime dateTime = format.parseDateTime("Wed, 27 Mar 2013 15:12:14 +0000");
When parsing this format a single Z
timezone character will suffice, 4 is invalid:
Z time zone offset/id zone -0800; -08:00; America/Los_Angeles
For more see the javadoc