The antenna is an easy fix. Snip it off at the top of the base and drill the base for a short piece of piano wire. It's the scale thickness and it doesn't have a too-shiny finish. I use piano wire for all my antennae. I just polish it up soime for non-beater models.
As for the badges, hit 'em with a wash of thinned flat white paint and they should come up looking like faded plastic emblems.
One more thing that I would do is sand down the tire treads. Those tires make it look like someone has started in on fixing it up by replacing the old-worn-out tires the car had been sitting on for all those years. Of course, that's a possibility too, but then the wheels would probably look better as well...