Plot hole: The plot of this film relies on the notion that Cutter and Ritter (with the backing of the President) are able to conduct this illegal war against the cartels with this small team of soldiers blowing up planes and drug bunkers while making it appear to be coming from rival cartels. OK, fine. The problem though is when you bring an aircraft carrier into the story a lot more people are going to have to know what's going on that are not in the loop. You would have admirals, navy officials, possibly even the Joint Chiefs wanting to know why planes are taking off from one of their aircraft carriers just outside of Colombian waters. It didn't take Ryan any effort to find the operations report on the "car bomb" and put two and two together, so I find it very hard to believe none of the higher ups in the Navy were questioning Cutter or the President as to what was going on.
Factual error: It wouldn't have mattered that Ritter had his "autographed get out of jail free card" given to him by Cutter or authorized by the President, it was still an illegal operation that Congress didn't know about. Anyone involved in it would be going to prison regardless of position.
Plot hole: Given the lengths that Escobedo is willing to go deal with people who have wronged him it's pretty hard to believe he would have wasted his time imprisoning the rest of Clark's team instead of killing them, especially after they caused so much damage to his cartel.