For example, I know that WWI started in 1914 and ended in 1918, but I cannot remember the months or dates. It really sucks because I love history but cannot have a conversation about it with anybody because it looks like I do not know what I'm talking about.
Honestly, dates aren't that important. Yeah, they're good to have in a paper, but you could easily look them up.
I think the most important things is to be able to place it in context. Is it the end of the world if you don't remember that Vicksburg fell on July 4, 1863? No. But you should know that it did happen the day after Gettysburg and its overall affect on the war.
What day did Columbus leave Europe in 1492? Who really cares. Just know that it happened the same year that Spain expelled all of the Jews out of their country and finished the Reconquista.
As a historian I have few conversations about history that hinge on dates, especially months/days. Most of historical study is examining change over time. Dates are important in that they order that study, but the meat of historical analysis has nothing to do with dates. It has to do with trying to understand the past, why things happened, how things changed, etc. In most cases, dates can be looked up as needed. When I was teaching Western and World History surveys there were only a few dates (years) I wanted students to know (mostly because it meant they knew the thing that happened in those years) 711, 1492, 1588, 1648, 1776, 1789, etc.