More pictures after the break...
The picture up there is from Out of Gas, when Wash interviews for the pilot position. Here's the back of that particular shirt.
We first see this shirt in Shindig, though I believe it is the same fabric, but a different shirt. The patterns are in different places:
and Heart of Gold:
The first tropical shirt we see Wash wear in the run of the series is in Bushwhacked.
The other shirt that appears in Shindig is this one:
It also appears in The Message:
A promo/signed picture:
A nice tropical shirt shows up in Safe:
We see the same one in War Stories:
I think it also shows up in Jaynestown:
This shirt (I think!) appears on the DVD menus:
This shirt is in Our Mrs. Reynolds, but I haven't gotten a very good picture of it.
My guess is that it is this shirt, from Trash:
As far as I know, this shirt in the following promo pictures was never used in the series:
I'm sure I've made mistakes or even missed one. But, I'll keep my eye out!
My Photobucket album for Wash.