Contradictions between delivery or body communication and the message of the speech can be when someone's tone doesn't reflect what they're speaking about. If someone is speaking about something serious, but they're speaking about it in a joking tone or even a less energetic tone, then that can give the impression that the speaker doesn't care about what they are speaking about. The way that people dress compared to what they speak about is also a big thing. If somebody gives their best man speech in some concert tee and cargo shorts, it's going to look like he doesn't care. However, I think that sometimes, a speaker who has put effort into working out how to contradict their delivery with what they are speaking about can be really cool. I feel like this would work best in a humorous setting. If a speaker is passionately explaining why smooth peanut butter is better than crunchy peanut butter, and it's meant to be funny, then that works. Overall, contradictions between delivery and message should be avoided, unless the speaker has developed a purposeful way to contradict their delivery and message in a way that is appropriate.
I agree that when people joke about serious things in a speech it makes it seem like they don't care. It makes me less likely to continue listening. I also like how you said that contradictions can be acceptable in humorous speeches too!