Perhaps the most obvious observation regarding the Joker’s shirts is that he had two: an orange one, and an emerald green one.
Although he actually wore the green shirt more often than the orange one in the movie, the orange one has since arguably become the more iconic and recognizable of the two – probably because the scenes/sequences with the orange shirt were longer and/or more memorable than many of the scenes/sequences with the green one (most notably the parade climax and final confrontation in the cathedral).
Although in the film the shirt collars appear to have had no topstitching, a Film Memorabilia auction viewing photo reveals that there was, in fact, a row of edge-stitching along the collar of the orange shirt.
Additionally, this photo of a screen-used Joker costume display at the BFI reveals similar edge-stitching on the collar of the Joker’s green shirt.
Here are a couple excellent photos of the Joker’s costume at the BFI display, in which you can clearly see the fabric, color, and buttons in better detail. (Special thanks for Paul Wares for the photos!)
Unfortunately, we never got a look at the back of the Joker’s shirt in the movie, so I can’t say whether or not the back of the shirt had a yoke and/or pleat(s).
The French cuffs on the Joker’s shirts appeared to be fairly tall (although not as tall as those on the 11th Doctor’s “Snowmen” shirt).