The worst mistakes of the Bush presidency were trying to correct the mistakes his father made.
Lots of people are saying the presidency of George W Bush was the worst in American history. I think it's way too soon to say such a thing, but he certainly didn't have an easy eight years either.
After serving as Vice President, George H Bush ran for President and uttered this phrase "read my lips, no new taxes." He was elected, and as president he chose not to veto a democratic backed bill that raised taxes.
It actually was a pretty good bill and was a direct contributor to the budget surplus of the Clinton administration. The republicans hated it though and saw it as a betrayal of their Republican ideals, which many think was a significant factor leading to his unsuccessful run against Bill Clinton.
When George W Bush became president, he saw this as indicating he should never cooperate with the Democrats in congress. Although he ran for president as a "uniter", once in office, Bush almost never reached out to the Democrats unless he knew they were already on their backs. This policy of not crossing party lines made Bush one of the more divisive presidents in the last hundred years, which is ironic because his predecessor, Bill Clinton, was most successful when he crossed party lines.
The other time Bush tried to correct what he saw as his father's mistakes was with Iraq. Republicans had long criticised George H Bush for not ousting Saddam Hussein during the first Gulf War. Bush said he did not have a UN mandate for ousting Hussein and they had achieved the primary objectives of the war to push Iraq back within their own borders, so he brought the troops home.
When George W Bush became president, he was overly eager to oust Hussein at the first sign of trouble in the middle east. After 9/11 Bush had overwhelming public support for pretty much anything he wanted to do in the middle east so he chose to invade Iraq based on some pretty shaky intelligence.
Once in Iraq, he learned that ousting Hussein was fairly easy, but rebuilding a stable country out of Iraq afterwards was very, very difficult.
One of the benefits of putting term limits on the U.S. President is that they can't go back and amend what they see as their earlier mistakes. Each new president starts with a fresh slate to make his own unique mistakes.
The term limit legislation didn't foresee a son following his father as president, though, or that the son might want to revisit his father's decisions. This may not be a situation that comes up very often, but it's worth remembering when it does.