So, for what it's worth, the fonts don't look strange for me anymore. I switched from Linux Mint Cinnamon to Linux Mint XFCE, reinstalled PlayOnLinux, and now everything is fine with the default version of wine (before I had to go to 1.4.1 to avoid blocky-looking fonts). I also tried 1.6.2, which was giving me problems before, and that one works fine too. So, I don't know if that's really helpful for anyone, but at least it's working for me.