I am using TeXmaker on a MacBook Retina with an additional external display. The documents displayed in the PDF viewer while on the external display are very grainy/blurry and hard to read, while they are completely fine on the MacBook screen and when opening the produced PDF with another software. I didn't find anything related to this online.
I had the same issue and found a work around. Open texmaker on your laptop's screen and adjust the size of the program window so that it fits the external screen (or your needs). If you than drag the texmaker window to the external screen and do not (!) resize the texmaker window, the internal pdf viewer looks normal.
As you might have an external screen larger than the laptop screen, you have to fiddle a bit to first adjust the size of the program window on your laptop screen, but it is worth it. The good thing is that resizing the pdf size within the viewer is fine.