I have also been having issues with the SWTOR installer.
Try installing xQuartz from xquartz.org
After I did that it let me progress to the next error messages from the Play On Mac interface.
I selected to download the Mono package & the Gecko thingy... I assume these are ok?
Also, when it asks, download or use the SWTOR installer on your computer, selecting download seems to work better.
(results in 2 MDS checksum mismatch messages).
Only when I try to RUN it the error message pops up (from SWTOR): "Certificate Authentication Failed. Please contact customer support."
And there's a little black screen that reads "Waiting for swtor..."
So... yeah it doesn't seem to work.
Edited by Ranger883