In "First Scandal," Mac issues an executive order creating a scholarship program for college students who agree to become public school teachers. Such a program would require a law to be passed by Congress; the President's executive orders only apply to the inner workings of the Executive Branch.
In "The Mom Who Came to Dinner," Mac agonizes over whether or not to commute the death sentence of a woman who was convicted of murder in Texas. In reality, the President's pardon power only applies to federal crimes.
In "Ties That Bind," Mac essentially federalizes law enforcement in Prince George's County, Maryland, sending in the FBI to investigate murders over which the federal government has no jurisdiction. No, the President can't do that, either.
Crowning Moment of Awesome: The speech Mac gives at the end of the first episode was worthy of a Sorkin script, and Geena Davis lent it just the right air of gravity without crossing into melodrama.