Plot hole: When Brody is flown back he is wearing his uniform, complete with medals and name. But he has been missing for 8 years! Where is that uniform coming from? Not from his wife, because she just heard from him. (00:04:00 - 00:10:00)
Suggested correction: It would have been provided by the military, when he was cleaned up, debriefed and looked after immediately after his rescue. It's mentioned that he returns to the US via a base in Germany, I believe.
Continuity mistake: Just before Carrie is told Brody is going to Bluemont Park, Carrie is shown re-watching Brody's welcoming ceremony on her laptop with the speech the Vice President gave and the speech Brody gave. The footage Carrie is watching on her laptop isn't the same as when the ceremony was broadcast earlier in the episode. The footage on the laptop has the Vice President saying "Sergeant Brody, you're a man who's endured a terrible ordeal" followed by Brody walking up the podium saying "Thank you, Mr. Vice President." But what was shown earlier was the Vice President welcoming Brody home, nothing along the lines of "Sergeant Brody, you're a man who's endured a terrible ordeal." Also, the length of time Brody spent walking to the podium and saying "Thank you, Mr. Vice President" has decreased when re-watching the ceremony on the radio - the actual ceremony showed Brody walking up to the podium for about 3-4 seconds followed by a 1-2 second delay before saying "Thank you, Mr. Vice President", but re-watching it on the laptop, Brody walks up to the podium and says "Thank you, Mr. Vice President" all within a split second of replying. (00:19:40 - 00:37:40)