Okay. So apparently, when playing at 720p (1280x720) resolution, FSO, in its infinite wisdom, decides to use the low-res interface, the one normally used for 640x480 and 800x600 resolutions. While this is slightly annoying in the menu part, it becomes downright obnoxious during gameplay:

There's a very simple fix for that, in 2d.cpp, line 381, change from
if ( (width >= 1024) && (height == 600) ) {
to
if ( (width >= 1024) && (height >= 600) ) {
Oh, the screenshot is slightly distorted, this was something that happened on the users comp, not an issue with FSO.