If you're running the game on an older computer or a laptop, you may notice some "lag" or low framerates (game feels sluggish). If this the case for you, you may be able to improve the performance by disabling various graphical options. Open settings.txt in your documents folder (see this article for where to find it) and change lines to read as below (you should experiment with these, not all will necessarily help and some will reduce map features).
Note that EU4 is less forgiving than CK2 for under-spec video cards in particular. If none of the above helps you can try any of the low-res mods in the EU3 User Mods forum; also is it presumed and hoped that Paradox will further optimise EU4 performance in upcoming patches (1.1.3 was just release at the time of writing this, so after that). There is no known fix or workaround just yet for the month-start hesitations, nor for the autosave lag in Ironman mode.