In one shot, Dr. Phlox hands T'Pol a dish with handles on the side. In the immediate next shot, T'Pol's hands have completely changed position.
After the alien gets up and attacks Flox , he phases through Flox's neck. And then he proceeds the phase through the wall. Since there is gravity pulling him toward the floor, he should have phased down through the floor.
Major Hayes calls Lt. Reed "sir" multiple times in the manner of speaking to a superior officer. However, Hayes is of a superior rank to Reed and should never do so. They obviously didn't realize that a Navy Lt was inferior to an army/air force/marine rank of major. (However, as two 'martial Gentlemen', he's using it as an 'address', not necessarily rank/status'.)
The use of stunt doubles during Malcolm and Major Hayes' fight scene is obvious.
When Cap Archer is dressing down Maj Hayes and Lt Reed, he addresses the severity of their injuries: "You have a detached retina. And you have a bruised kidney." Have, not had, so it hasn't been fixed yet.
He would not have him standing there at attention with a detached retina. He would be in surgery as immediately as possible upon discovering the detachment, in order to avoid immanent vision loss. Unless this risk has been reduced by medical advances leading up to the 22nd century.