I try to convert a string into a datetime:
String dateString = "2015-01-14T00:00:00-04:00";
DateTimeFormatter df = DateTimeFormat.forPattern("yyyy-MM-dd'T'HH:mm:ssZ");
DateTime dt = df.parseDateTime(dateString);
If I display dt.toDate()
I get: Tue Jan 13 23:00:00 EST 2015
So there is a time problem.
Without the DateTimeFormatter, I get the same issue.

It's getting the correct value - basically 4am UTC, which is midnight in a UTC offset of -04:00 (as per the original text), or 11pm on the previous day for EST (as per the displayed result).
The problem is that you're using java.util.Date.toString(), which always returns the date in the system time zone. Note that a java.util.Date only represents an instant in time - it has no notion of a time zone itself, so its toString() method just uses the system default.
If you want to retain the time zone information (or in this case, the offset from UTC information - you don't have a full time zone) then stick to DateTime instead of converting to Date. Ideally, avoid java.util.Date/java.util.Calendar entirely. Stick to Joda Time and/or java.time.*.
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