When Data escorts Ishara to the transporter room for the final time, they enter with her on the right and him on the left. When the shot changes to inside the transporter room, suddenly he is on the right and she on the left.
When Ishara is describing the Alliance fusion source to Data on the bridge, she points to the computer to show him the locations of various entry points to a specific chamber on the cartographic display. In the reflection on the monitor, you can very clearly see that Ishara's lips are not moving as she continues to speak. Furthermore, the actors portraying both Data and Ishara appear to be possible stand-ins for Brent Spiner and Beth Toussaint respectively.
When Dr. Crusher takes a DNA sample from Ishara, she says the test to see if Ishara is related to Tasha will take a few hours. However, other instances of DNA being analysed had nearly instantaneous results.
Troi should have been much more capable of detecting Ishara's deception.
The proximity sensors make no sense. Why would anyone implant something that would alert an enemy when encroaching on their territory.
Hayne asks for all the information they have on the Enterprise, but as Riker stated they hadn't been able to maintain reliable communications since their government fell, and the colony cut off all contact with the Federation in 2352. So they wouldn't have any information on the Enterprise-D, which was launched in 2363; at the time they broke off contact with the Federation there wasn't an Enterprise in service with the Enterprise-C being destroyed in 2344.
When talking to Ishara on the bridge, Data talks about Tasha becoming close to "myself". Grammatically this is incorrect, he should have said "me" as he is the object pronoun. For someone who is impeccable in language including lack of contractions, this is an odd mistake.
When Riker's away team first encounters the Coalition raiders, he states that they're from the USS Enterprise and that they're looking for two of "our" crewmen. The men they are rescuing are from the Federation freighter Arcos; they are not from the Enterprise.
On the bridge near the end of the episode, Picard says that each of them was to blame for being so willingly deceived, apparently forgetting that Troi had twice warned him of a deception.
When Ishara beams aboard the Enterprise, she is greeted by Data. As the two of them discuss her sister, Ishara says that Tasha left the colony because of cowardice. Data replies "Cowardice is a term I've never heard applied to Tasha." Data very clearly uses a contraction.
At one point, Picard refers to Hayne's coalition as "Haynes's coalition".