What were the fundamental mistakes committed by the Americans in initially becoming involved in the Philippines?
If we assume that the US did make mistakes when deciding to take the Philippines in 1898, we can say that there were two kinds of mistakes.
First, the US erred in thinking that it was justifiable to take control over another country that wanted its freedom. This contradicted basic American values.
Second, the US erred in thinking that taking the Philippines would make the US stronger overall. Americans thought that having bases in the Philippines would help to project American power. As it turned out, possession of the Philippines only served to get the US involved in WWII since US outposts in the Philippines seemed to threaten Japan's ability to take the empire it felt it deserved.