While taking the wild turbolift ride to the bridge, a line of sweat appears on La Forge's back. But when he's thrown onto the bridge a moment later, the line of sweat is gone.
When the Romulan ship appears over Iconia, Riker orders shields, prompting Wesley to act, but shield control isn't maintained from Wesley's console. It's from the tactical station.
Data informs Picard that the ETA to reach the Iconian's planet at warp 8 is 12 hours and 16 minutes. Picard then orders his crew to head for the planet at warp 8. After the Enterprise arrives at the planet, Data says that the alien virus has managed to reprogram the computer to a dangerous point in less then 7 hours, but the virus infection happened when they were connected to the Yamato; so, before the Enterprise jumped to warp, it would have been at least 12 hours that the virus worked to reprogram the computer, probably more.
When Picard browses through Donald's log, you can see it is ordered by star-dates. The computer searches from top to bottom, so every log-item should go from past to future. At one moment you'll see Donald talking about his first officer questioning his order to violate the Neutral Zone. This log-item is made on star-date 42607.33. When the camera switches between Picard and the computer, the log-item is suddenly 42607.95. After that, the computer finds the next log-item, star-date 42607.33 again. The bug is not still over: when the computer finds the next log-item, the log-item shown in the list-view is 42608.3. When the computer opens this item, it is again star-date 42607.95.
In Where Silence Has Lease (1988), the Yamato's registry number was NCC 1305-E. Now, in "Contagion," it has become NCC 71807.
When the turbolift goes crazy with Geordi bouncing around in it trying to get the bridge, you can see where the paint has come off of the upper area from previous takes.
Geordi closes Data's eyes, but it's clear that Geordi's hand is too far from Data's face to actually do this.
When Worf appears on the Enterprise bridge carrying Data, he says that they must get Data to engineering. The next line, "Hopefully, the captain will follow," is heard, but Worf's lips are not moving.
The first time Picard says to raise shields, the red alert sound activates. The second time, no alert sound is heard.
Doctor Pulaski has to explain the concept of a splint to a fellow doctor when the Enterprise's computers start malfunctioning. Given that Starfleet Academy requires its cadets to learn how to survive in a wilderness with minimal technology, it seems odd that Starfleet Medical wouldn't require its medical students to learn low-technology medical techniques.
Worf is able to detect the Romulan ship at long range while it is cloaked. This is inconsistent with other episodes where Romulan and Klingon ships can close to within a few thousand yards undetected while cloaked.
The Iconians made it too easy for anyone to come along and destroy their facility full of probes. All Picard was required to do was hit the blue button three times to complete this task.
When Picard orders Worf to destroy the probe, the microphone's reflection is seen in the engineering station at the back of the bridge, moving left to right as Picard and Worf say their lines.
Riker continually calls Sub-Commander Taris "Toris," even when Counselor Troi correctly pronounces the name Taris properly.
When Riker, in command while Picard is off the ship, follows Worf, who carries Data into the turbo lift, he never tells anyone else to take command of the bridge. This is always done when the ranking officer leaves.
When Data throws Geordi away from the malfunctioning Pult, he intensely reacts to the stunt like he was surprised and worried. This does not match the inability to feel emotions that Data has.
While investigating the gateway, Data uses the word holograph instead of hologram.
When Picard is beamed back to the Enterprise from the Romulan ship, he calls the bridge immediately to give instructions but states "Bridge to Picard". It wasn't "Bridge from Picard". Patrick Stewart reverses the line. He should have said "Picard to Bridge "...