When Garcia and Morgan are first going over the bomb fragments, Garcia says her father wishes she had chosen medical school instead of the FBI. In a later episode, it's revealed that her parents were killed when she was a teenager as they went out looking for her in the middle of the night.
In the newspaper article, it states the bomb blast happened in an apartment building. Gideon says it happened in a warehouse.
When Hotch is talking about collecting coins, he says that he spent a lot of time searching for the 1944 penny. In reality, the expensive one he would have been looking for is the 1943.
When the BAU in Palm Beach receive the information about the three bombs matching the bomb of the guy who blew up some FBI people in Boston, Gideon sits down and grabs a water bottle with the brand name "Poland Springs". In Palm Beach, FL, this would have to be imported. The same parent company owns the names "Poland Springs", "Arrowhead", "Deer Park" and "Zephyrhills". The latter is the water that is distributed in Florida, while Poland Springs water is distributed primarily in the American north east.
On the front page of the Boston newspaper shown near the beginning, the second column of the article is the same information as in the first. Word for word.