For example, you'd go directly to Joda-Time or JSR-310. Date and Calendar wouldn't be present at all.
Whether Java should break compatibility to remove all the old cruft I'm not sure. The benefits of the cleaner design might not be worth the costs/inconvenience.
It's like Soupstrain said: there are only two kinds of languages: the ones people complain about and the ones nobody uses.
A side effect of success is having a large body of existing code to consider when making changes.
Things which come to mind (comparing roughly 2.8 (released 2010-07) to 2.11 (released 2013-03)):
Classes (just from the top-level scala.* package):
- scala.actors and subpackages
- scala.concurrent (still exists, but its contents have been replaced completely)
- scala.dbc and subpackages
- scala.swing and subpackages
- scala.util.parsing and subpackages (includes parser combinators and JSON)
The list is certainly incomplete anyway...