Lech Lecha 5778

The Ramban points out in two places where both Avraham and Sarah both erred in their actions. At the beginning of the parsha, Avraham leaves Israel in order to find food in Egypt during the famine. The Ramban mentions that he did two things wrong. One was that he put his wife in a dangerous situation; by saying Sarah is his sister, that would only entice others to take her even more. The other was leaving in the first place; Avraham had shown a lack of faith in G-d and His being able to provide food for him. Because of this, his descendants would also leave Israel for Egypt only to be enslaved for hundreds of years.
Sarah also erred in her treatment of Hagar. As tension grew in the household, Sarah began mistreating Hagar to the point of Hagar running away. The Ramban says she did a grievous sin doing so. Because of this, Hagar's descendants would be destined to mistreat and be harsh with Sarah's descendants to this very day.
The Torah points out the mistakes of the patriarchs and matriarchs to teach us proper conduct. It also shows us that they were human despite their holy status. This allows us to strive to reach their level without thinking of it as an impossible feat.

Noach 5778

The Kli Yakar suggests that the people who built the Tower of Babel had the right idea to do so. They were worried that if they separated into different communities, they would wage wars with each other. However, they erred in saying that they wanted to make a name for themselves as well. Everyone had their own way of doing so; some wanted to become rich while some wanted to have all the food in world. G-d knew that bringing wicked people together would only split them apart, as they would attempt to rule over each other and engage in a civil war. They would be more united if there was a bit of separation between them.

This is based on the Talmud in Sanhedrin (71b) that says a gathering of wicked people is bad for them and for the world while a gathering of righteous people is good for them and good for the world. Righteous people have only one mission and can therefore join together in the service of G-d. However, there are many ways to be wicked. G-d's punishment of dispersing them was really a blessing in disguise.