The Big Tick - S2-E2
Factual error: When Gwen and Grandpa Max use the shell plates from the tick to ward off it's corrosive secretions, their fingers should have been eaten away since they were grabbing the rims of the plates when the acid came raining down.
Back With a Vengeance - S2-E13
Factual error: It would be highly improbable for Kevin to find Vilgax frozen deep in space. As we see in first season's episode 'Secrets', Vilgax's ship was blasted apart in the upper atmosphere - after all, Ben escaped as Heatblast, and he wouldn't have been able to once beyond the stratosphere. Earth's gravitational pull would have kept Vilgax on Earth, not released him into deep space.
Plot hole: In Ben's nightmare, Gwen says, "We will come and get you!" and then she nags at Ben for being the one with the alien powers, and she does not join him in climbing the tree. My guess is that this was due to a script error; it was likely supposed to be "he" (i.e. Ben) instead of "we".
Factual error: When Enoch is seen with the dust which has once been the sword, there is a larger dust pile than the sword blade would have left on the floor.
Factual error: When Ghostfreak first escapes the omnitrix, right before he rips off his outer layer of skin, he still has the omnitrix logo on him even though it should be gone with him being outside the watch.
Continuity mistake: When grandpa Max first wakes up in the fungi cave, we find him completely wrapped in tendrils. But when XLR8 comes to cut him loose, Max' shoulders are suddenly free.
Continuity mistake: When Ben, Gwen and Max try to track down Ghostfreak, Max's scanner picks up "trace spectral activity from around that corner", which happens to be right ahead, but then Ghostfreak and cohorts appear from behind. In a deleted scene featured on the series' DVD, the source of the reading is revealed to be the tuba player Ghostfreak had possessed, who instantly runs off at the sight of Fourarms.
Back With a Vengeance - S2-E13
Plot hole: It is rather strange that grandpa Max would have a kid-sized Plumber suit ready for Gwen, given a) that the Plumbers are effectively defunct, and b) that a government organization would hardly allow underage trainees in their ranks.
Other mistake: Gilbert is the only one to have a name tag, whereas Andy and Mandy don't - rather strange for a summer camp where dozens of kids tend to run around to issue tags to only some of them.
The Galactic Enforcers - S2-E6
Other mistake: Generally, voice actors are listed only by the roles which they actually perform in the respective episodes. Even though Ripjaw's voice, Fred Tatasciore, voices Cannonbolt and others throughout the series, the character of Ripjaws does not appear in "Galactic Enforcers" and thus should not be listed in the credits.
Continuity mistake: Fourarms Gwen launches four bowling balls with all her arms at the same time, but the balls strike the pin sets one at a time.
The Galactic Enforcers - S2-E6
Other mistake: In the end credits, one of the characters listed is Ripjaws, who is, however, actually not featured in this episode.
Other mistake: In Ben's dream, Wildmutt's brace is the same color as his body while Ghostfreak grabs him.
Other mistake: Grey Matter held his breath underwater to save the drowning man, but he has gills so that he can breathe just like fish.