When Klaang is returned to Kronos, another Klingon cuts his hand with a knife to get a blood sample. The viewer sees red blood. However, as established in Star Trek: The Undiscovered Country, Klingons' blood is pink.
Silik, being aware of the effects of the communication room's temporal distortions, tells Archer it would be unwise for him to discharge his weapon in the room. Yet when Silik takes Archer's phase pistol he fires it and experiences the very thing he was warning Archer to avoid.
In the early scene at the medical bay, Captain Archer says that the Vulcans have been holding Star Fleet back for 100 years. However, this takes place in 2151, and the first warp flight was in 2063, only 88 years ago. The Vulcans never made contact 10 years in advance of the first warp flight because it was against their rules. However, Archer may have just been using 100 as a point of emphasis in his discussion with T'Pol.
In the opening shot of Kronos, the CG figure walking by the base of the bridge with a sword-like object in their hand can be seen to "ascend" one step before it actually reaches the area with the steps leading up to the bridge.
About two thirds of the way through, T'Pol can be seen staring into a blank display screen and reading off coordinates as if she saw them on the blank screen.
When Captain Archer travels to Brazil, Hoshi Sato is teaching a class in another language. The closed captions state it is Klingon, however, since Earth hasn't had any contact with Quon'os before, it is highly unlikely they would know how to speak it, Hoshi tried to use the universal translator when Klaang is in sickbay. Since she wasn't familiar with any Klingon dialects, with the small sample the Vulcans donated, the language she was teaching was another species, possibly insectoid.
Shortly after departure, Captain Archer states they will arrive at Kronos is ~80 hours. He later states they are traveling at 30 million km/s. That is 100x the speed of light, which means they would be traveling at just above warp 4.6, though he was likely stating an approximation, and they were actually traveling slightly slower. However, even at 30 million km/s, they would only travel ~0.91 light-years in 80 hours, which wouldn't even get them to our nearest star, Alpha Centauri (4.367 light-years away). It would take 16 days just to get there at that speed.
T'pol describes the planet Rigel as being "approximately 15 light years from [their] current position." After the Enterprise travels to the planet, Captain Archer describes Klaang as having been on Rigel "just a few days ago," but even at the then-maximum rated speed of the Enterprise engines, Warp 5 (214 x light speed), it would have taken the ship about 26 days to travel to the planet, making the Klingon's meeting a month or more in the past by the time they arrived.
The location is said to be Broken Bow, Oklahoma, and a sprawling cornfield is shown. Oklahoma isn't even in the top 10 for corn production so a large farm like this would be unusual. The biggest issue is that Broken Bow is in the Ouachita Mountains. The topography is totally wrong. Also, that area of the state is known for its huge pine forests where companies like Weyerhauser have lumber yards and paper mills. In fact, Weyerhauser owns most of the land there for pine tree production.
Star Trek has often been inconsistent regarding the ability to go to warp within a star system. Doctrine in Star Trek: Deep Space Nine (1993) says it can't be done. However in Star Trek (1966) and the TOS movies, they routinely went to warp inside the solar system, most notably in Star Trek III: The Search for Spock (1984). It is highly illogical that Kirk and Archer could routinely go to warp inside solar systems, and apparently the later presumably more advanced star ships could not.
Captain Archer mentions that a "7 foot" Klingon would be hard to miss on Rigel 10. In Star Trek, the metric system is used, therefore his height would be referenced in meters and not feet. Also, Klaang is only 6"5.