Plot hole: Jack is informed that experimental treatment using stem cells from a genetically compatible donor is being developed that might be able to cure his condition. Stem cells are used to treat diseases where a cell type in the patient's body malfunctions, such as insulin-producing beta cells in diabetes, or where injury has killed cells that do not regenerate, such as in spinal cord injury. In these cases stem cells can replace the damaged cells and make sense as therapy (bone marrow transplant as leukemia treatment is one real such treatment). Prions (which is what the show calls the bioagent) and bacteria (which is how the show describes the bioagent) cannot be cured by stem cells, since the cause of the disease is not damaged or defective cells. Even if the disease damaged brain cells and stem cells cured that, it would resume later since the causative agent is still there.
Continuity mistake: When Agent Walker enters the building where Matobo is being held, Chloe tells her on com the stairway is to Agent Walker's left, she then immediately goes to the door to her right to enter the stairwell to let Jack Tony and Bill in from the roof.
Plot hole: The director of CDC informs the cabinet that the biological weapon at hand is a "prion variant indigenous to the East Congo" and refers to it as a "strain". A prion is a protein, not a bacterium, so it cannot be indigenous to a certain place and cannot belong to any strain. More importantly, prion diseases are not known to be transmissible in an airborne fashion (Mad Cow and Kuru, also prion diseases, are transmitted by ingestion), which kinda takes the air out of the threat. However, the description of prion disease symptoms and the example of Creutzfeldt-Jakob disease as being caused by prions are accurate.
Continuity mistake: In the season finale of 24: Day 7 when Tony is torturing Alan Wilson and Jack comes in and shoots Tony in the shoulder, we can see Wilson raise his hands while lying on the floor with his legs to his left. Wilson remains in this position when Jack shoots Tony in the knuckles. Directly after the shot of Jack shooting Tony in the hand, we can see Wilson sitting cross-legged. With the time elapsed, he had no time to change into his position that quickly. (00:19:50)
Plot hole: The head scientist tells Tony that they need Jack's organs to reconstitute that pathogen since there is not enough of it in the sample. Assuming it's a virus, even a small sample could easily be grown in the lab to yield large amounts of the virus. Assuming it's a prion, they don't even need a sample since the could simply build it again from scratch so long as they knew the protein sequence (which is a likely assumption). In either case, Jack is unnecessary.
Continuity mistake: When president Taylor asks Olivia to be her acting Chief of Staff, Allison rests her head on her hand, with only her elbow on the couch. In the next shot, her arm is suddenly resting on the couch instead. There's a straight cut between the two shots, so she didn't have time to move. (00:10:55)
Continuity mistake: When the terrorist keeping an eye on Kim bends over to move his baggage for other people to sit down, Kim notices his neck is bleeding from him confronting and killing the FBI agent watching her (which she doesn't know). However, in the last 15 minutes of hour 5:00AM to 6:00AM, when he kills the FBI agent, he doesn't receive a scratch. (00:05:55)