When a flashback of April 2006 is shown, Lily is shown with the long dark hair which she had after coming back from San Francisco in the fall of 2006 rather than the shorter red hair she actually had at the time.
While Barney is sitting on the subway and speaks with Ted, the subway moves from the left to the right. But when Barney arrives at the station, it moves from the right to the left, which means it would have changed the direction.
No one can just decide to run the NYC Marathon. You must run and meet a qualifying time with a qualifying running organization. Marshal may have done this, but Barney would not have had enough time.
During scenes at the airport while waiting for a flight, the exterior visual clearly shows an airliner in Air Cal livery. Air Cal was a) an airline devoted to intra-California service so wouldn't have been at La Guardia and b) ceased operations in 1987 - 20 years before the episode.
During a scene set in 2006, footage of the outside of La Guardia airport is shown with Delta planes decorated with pre-2000 livery.
In one of the first shots we see an airport terminal building with some planes parked in front of it. One of them is clearly a Swissair plane. This former Swiss national airline ceased to exist in 2002, five years before the scene takes place.
When Marshall is talking to himself in the mirror, the rest of the reflection is of the kitchen and not the living room where he is.
At the closing of the episode, when talking about how it was his destiny to stay in New York and meet the Mother, he is shown wearing a tux with Barney and Marshall in a church-like setting, but the scene is not like that shown in the Finale where he is marrying the Mother.
Ted says "Do you realize this penny was minted during World War II?" about his penny from 1939. World War II started in September of 1939, so Ted shouldn't have been so sure about his claim.