In one of the final scenes, with Picard and Data heading to the Bridge in a Turbolift, Picard wears only the 3-pip rank of Commander, but when he steps out of the lift, he again wears his rightful 4-pip Captain rank.
In the mud bath scene, the amount eaten of the edible cups changes several times between shots.
In the mud bath, the mud covers the back of Lwaxana's right hand in some shots but the hand is clean in others.
Upon arriving at the asteroid field, Data instructs the computer to emit a hydrogen/nitrium plasma beam from the Enterprise's Bussard collectors (located on the forward end of the warp nacelles). However, the plasma beam is shown being emitted from the saucer section's ventral phaser bank.
Geordi says that the residue created by the parasites "was elements broken down into simpler molecular structures". However, a chemical element is the simplest atomic structure there is. The only thing an element can be broken down into is subatomic particles (proton, neutron, electron). Also, a molecule is a more complex structure; it is made up of multiple elements. Geordi probably misspoke and meant to say "the molecules in the residue were broken down into simpler elements".
As Picard and Data discuss the time it would take to reach the Pelores asteroid belt, Data states it would take over five hours at Warp 9, but a few minutes later on the bridge it's stated that it would take a little over three hours at Warp 6.5. Given the logarithmic scale of each level of Warp, the time at 6.5 would have been weeks or months at the very least to reach the asteroid belt.
When discussing how to potentially slow down the progress of the metal parasites, Data suggests they try an exanogen gas barrier which would use extreme cold to hinder them. Since the parasites were picked up from an asteroid in outer space, cold would have no real effect on them, given their customary environment.
An unknown and potentially fatal situation is occurring on the Enterprise, yet Captain Picard allows important people to beam aboard and he doesn't even explain the situation.
Visible at the top of screen, when Picard and Riker discuss Lwaxana Troi's wedding while walking down a ship corridor.