When General Hammond is briefing Major Davis in the car on the way to the airfield, he states, "approximately 10 minutes ago, we established a wormhole to a planet at or very near the event horizon of a black hole." This is incorrect because Carter mentions previously that they have passed the 38-minute mark that the wormhole can stay open.
When Carter is briefing General Hammond on what will happen to SG-10 (their bodies ripped apart) one shot shows the video feed with all four members looking away from the camera. A few seconds later Col O'Neill references the face of one of the team members, shown facing the camera. This wasn't possible based on how slow time was moving on the black hole side of the worm hole.
When SGC starts receiving visual data from the probe, they must blue-shift the image to equalize the color. As the planet falls closer to the event horizon, the image should increasingly shift toward the red side of the spectrum, assuming no coding was input to compensate; an unlikely possibility.
If a star just turned into a black hole, then it would have just about the same mass and effective gravity as it did moments before. Just because the star turned from emitting light to appearing dark does not mean that time suddenly slowed to a near stop. The remote planet would be well clear of the event horizon, so the team on the planet would keep moving at the same speed the entire time and not experience time dilation.
O'Neill and Cromwell are provided with G-suits to help them combat the effects of increased gravity as they approach the Star Gate. G-suits work by inflating with air when g-forces increase, helping to force blood from the lower extremities back to the brain. O'Neill and Cromwell's g-suits aren't connected to anything, therefore they're useless.
The cold open is supposed to depict the heavier one of the dual stars sucking matter from its companion until the gravitational limit is exceeded and collapsing to form a black hole. While that is indeed possible (as far as current physical understanding surmises), the star collapse takes the form of a nova or even supernova, a huge thermonuclear explosion on a truly stellar scale. Time dilation would not be a problem on a planet orbiting a star that goes nova, but the intense radiation, debris and shock wave would annihilate any planet nearby within minutes.
Closing the iris on the Stargate would not prevent the gravity field to "get in" the SGC, since any object of any matter can not reduce gravity.
As a matter of fact, it would even theoretically increase the field, due to the iris' own mass.
S Carter states that "time within the SGC facility slowed to an average of about 600% below normal", which does not make much sense, as such.
And "when you ordered Col O Neill to wait 5 minutes, you were really telling him to wait 6 hours"... which is a factor of 72, not 6 (as stated with the 600%)
When Colonel O'Neill pulls the clip to set the detonator, it shows 02:00. Moments later it shows 00:20. However, in the first shot, the keypad is on the left and in the second shot is on the right, indicating the bomb has simply spun 180 degrees on the rope.
In scene 9, Stargate Command begins to experience the gravitational effects of a black hole located at the other end of the stargate's wormhole connection. This causes the Stargate event horizon puddle to rotate clockwise. However, this is a goof because, since the star-gate is located in the northern hemisphere, based upon the Coriolis force, the stargate's puddle should be rotating counterclockwise.
The Coriolis force is not strong enough to affect "objects" that small. just like the vortex in a sink can be turned with a finger, the direction is random. The rotation direction is more likely to be a result of the other gate's orientation to the black hole.
When the black hole's gravity destroys the glass and moves a chair toward the gate room neither the people or the computers appear to move in the same direction.
When Carter is introduced to Col. Cromwell, they exchange salutes. Salutes are not exchanged indoors except in the case of reporting to a commanding officer.
Carter states that "time within the SGC facility has slowed to an average of about 600% below normal". This is bad math. 50% below normal would be half speed, 100% below normal would not be moving at all and 600% below normal would be moving backwards at 5 times normal speed.