As Archer first starts to walk out into the auditorium to give his speech, T'Pol stops him. He turns back, holding his PADD in front of himself with both hands. In the immediate next shot, his hands are at his sides with the PADD in one hand.
The events of the episode are taking place within the Star Trek: The Next Generation episode The Pegasus (1994), which was made over a decade earlier. This is a bizarre choice, especially since both Riker (Jonathan Frakes) and Troi (Marina Sirtis) look noticeably older and heavier than they did in the original episode.
When Riker and Troi are talking in the conference room, after Riker plays the role of the chef, the stars are stationary despite the fact Enterprise is shown moving (likely at impulse). This is a goof seen repeatedly throughout all Star Trek series.
One of the CG shots of the Enterprise-D, it can be seen with small, white, glowing points of light which are supposed to be stars. The Enterprise is not so massive that a star appears that small by comparison.
Hoshi mentions that Trip never even went to college. However, Hoshi didn't actually say Trip never went to college, she said he didn't graduate from college. And this wouldn't necessarily have excluded him from attending Starfleet Academy (if the institution existed during the time of Enterprise).
At the beginning, Riker can be seen twice in Ten Forward, since Jonathan Frakes in 2005 was digitally inserted into a shot from Ménage à Troi (1990).
When Chef Riker kisses T'Pol, her head moves although she is supposed to be a frozen hologram.
During the shootout on Rigel X when Commander Tucker nearly falls from the walkway, the safety harness around his thighs is briefly visible in two different shots.
Where did Commander Riker get the chance to spend so much time on the Holodeck when so much happened in The Pegasus (1994)?
In the prologue, Travis says they've been on Enterprise for 10 years, yet he is still sporting an Ensign's pip. He should at least be a full Lieutenant by then, if not a Lt. Commander. In fact none of the senior officers have gotten a promotion.