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 Phlox he phases through Phlox's neck. And then he proceeds to 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 outranks Reed and wouldn't need to address him in such a way. The ground forces rank of Major is equivalent to the naval rank of Lieutenant Commander, whereas the naval rank of Lieutenant is equivalent to the ground forces rank of Captain. (However, as two 'martial Gentlemen', he's using it as an 'address', not necessarily rank/status'. Plus Reed's position as Chief of Security could give him seniority over Hayes.)
A person or object that is out of phase with space-time is able to pass through solid objects due to the fact that they are partially existing in another dimension where the laws of physics are different. So if being out of phase allows said person to bypass the normal laws of physics then in theory they might not be affected by gravity as well, hence why they do not fall through the floor when out of phase.
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.