Joe leaves a note for Danny and Jamie which Jamie says has "six numbers and 'R' and 'I'", which they figure out means that Joe and Dixon are in a vehicle with Rhode Island plates. But when Joe and Dixon are next seen, the vehicle they're in has Rhode Island plates with eight numbers.
Two Reagans are at a servo when the crooks pull in with two big utes. Danny pours sugary drinks into the fuel tanks of the crooks' utes and then Danny and Jamie take off. When the crooks go to chase them there utes stall almost as soon as they start driving. In real life they would have driven at least a few miles before the drinks mixed in with the fuel and got sucked into the motor.
Kenny jumps out of the truck during the big gunfight. The slide of his weapon is clearly locked back. Yet he does not seem to know it.
At Sunday dinner, Joe's saint Jude medal is returned to him. He is says it was his father's. Since his mother and Joe had a fling and Joe did not know she got pregnant. There is no reason he would have given her his medal. Therefore Joe would have had it from his father.
Danny and Jamie figure out that Joe is headed to Portsmouth, NH. They briefly meet up with him, allegedly there, however the Auto Repair shop in the background has a 516 Area Code which is Long Island, NY not 603 which is NH.
As per the Trivia entry, Danny (Donnie Wahlberg) corrects Jamie (Will Estes) on the pronunciation of "Worcester" (Massachusetts) as an inside joke on Wahlberg being a Boston native. As far as their characters go, however, Danny has lived in New York City his entire life except for military service, while Jamie attended Harvard University for at least seven years (four of undergraduate and three of law school) in Cambridge, MA, another Boston suburb, and would not be likely to mispronounce "Worcester".