What were the causes and consequences of U.S. entanglement with Mexico?
There were a variety of causes that led to US intervention in the Mexican revolution and they can be summarized as political and economical interests. The US was always interested in the economic opportunities that existed in Mexico and Latin America. It supported different Mexican governments and leaders until the Mexican Revolution introduced complexities in their relations.
US citizens including some of their leaders believed it was necessary to intervene in the Mexican revolution. There was need to protect US interests given the impending reorganization due to the revolution. Americans perceived Mexicans as violent and lawless hence a statement by President Woodrow Wilson that US intervention was necessary to stabilize the country.
US intervention in the Mexican revolution led to violence and skirmishes along the American-Mexican border. Supporters of the Mexican revolution from Mexico attacked US army barracks and the US responded by pursuing the militia into Mexico. This led to deterioration of US- Mexico relations.
Since this is in with some questions about Woodrow Wilson, I assume that you are asking about American "entanglement" with Mexico during the 1910s.
The main cause of this entanglement was the US's desire for a democratic government in Mexico. After the Mexican Revolution, Victoriano Huerta had ended up in power. He was brutal and had not been elected. Therefore, the US allowed weapons to be sold to his rivals. The US also seized the port of Veracruz to try to keep arms from getting to Huerta.
The major consequence of this was a worsening of relations with Mexico. Even the Mexicans who were getting help from the US did not like things like the occupation of Veracruz or Pershing's expedition in pursuit of Pancho Villa.