Many speakers can't resist the temptation to use big words while giving a speech. Sometimes it is a conscious effort to appear to be smart, sometimes it is an unconscious impulse because that's what a speaker thinks he or she is supposed to do in a so-called "formal" speech.
Either way, it's a bad idea.
Using big, long, or fancy words in a speech can damage you with your audience, not enhance your credibility. If you use a word that some or most members of your audience doesn't understand, you are creating a distance between you and the audience. At some level, audience members are thinking, "Hey, this guy thinks he's smarter than I am. Well, we'll see about that!"
Another danger of using big words is that you will seem insecure--it's as if you were trying to hard. A part of what made both Ronald Reagan and Bill Clinton master communicators is that they were always quick to edit out big words that a speech writer put into draft remarks. Both Presidents understood the power of simple words.
Yes, throwing big words around has helped some media figures like William F. Buckley Jr. But if your primary goal is to communicate a message (and not creating an aristocratic image for yourself), then you should stick to smaller, shorter, and simpler words.
Remember, it's not about dumbing down your ideas, it's about clarity.
Why use "mitigate" when "lessen" will do fine?
Why use "jejune" when "ordinary" does the trick?
Also keep this in mind,: there are many big words that people are used to reading, but aren't used to hearing. So if you say them out loud, it will take people a second to remember what they mean because they hear the word so infrequently. Better to use words that most people use in every day language.
This lesson is especially important for politicians. Winston Churchill prided himself in being able to give speeches on complicated foreign policy matters while never using words with more than two syllables. He understood that the ears process information differently than the eye does, and that the shorter the word the better for all speaking situations.
So if it's good enough for Churchill, then it's good enough for you too.