It receives traffic, but the traffic severity indicator on left is missing. It substantially affects the usefulness of information!
When the traffic receiver is plugged into another unit I have, a 255W, it shows up severity status just like I expect and I was expecting the same from the 1300 series after seeing this review:
http://www.gpsmagazine.com/2009/06/garmin_nuvi_1390t_review.php?page=8
This is how it shows up. This is a screen shot taken on my actual unit.

This is how I expect it to show up. This is form a review photo of 1390, which is the same as 1350 + Bluetooth. This is how it shows up as well when I hookup the GTM25 to my 255w

I have tried this here and it did not fix it.
buy.garmin.com/.../case.faces
Someone else complained about exactly the same thing here.
http://www.gps-data-team.com/pda-gps-navigation/viewtopic.php?p=13032
Customer service isn't very helpful.
After emailing support with links to photos, first they tell me they don't know what I am talking about and to clarify my request. The rep clearly didn't view the attached photos. I ask them to read the original request again and view the photos from attached links
Another rep responded
"Thanks for getting back with us. That feature is not something that is on that series of model. Some of our older units have it show up like that but the 1000 series doesn't show the traffic that way. If you have any further questions please let us know. "
So, they don't view linked photos in requests and they refer to 1300 series as the "1000 series" which I don't see in their product list. I wonder if they know their products all that well.