Corrected entry: It makes no sense for Clay-Face to fake like he lost control of his abilities in order to fake his death when he's close to killing Batman.
Corrected entry: Unless he didn't feel like it or Daggett's being held somewhere that's secret there's no reason that Clayface, who faked his death, couldn't try to track him down again.
Correction: There's absolutely nothing in the episode that suggests Clayface can't try to track down Daggett again. That's pure conjecture on your part. And conjecture is not a mistake or plot hole. But just to humor you, as seen in the series, Clayface goes through many other trials and tribulations that take up his time, which might explain why they don't show him going after Daggett in future episodes. Either way... this isn't a plot hole.
The Man Who Killed Batman - S1-E49
Corrected entry: It's never revealed how Batman saved Sidney from the vat of acid.
Correction: Sidney is telling his own story and doesn't know how he got saved. He said he must have been sucked down a drainpipe. Later when he finds out Batman saved him, he doesn't ask any follow up questions. The fact that it's never revealed has nothing to do with the plot and it's not a mistake.
Correction: Something not being explained is not a plot hole, nor is it any other kind of mistake. Batman, among many other things, is a ninja and an escape artist. We as the audience understand that he has the capability to rescue Sid the Squid from his predicament, and taking time to explain how he did it would just eat up screen time in what is only a 22-minute episode.
Heart of Ice - S1-E3
Corrected entry: Mr. Freeze's cell at Arkham Asylum has been modified to accommodate his inability to survive outside of sub-zero temperatures, but his cell has a barred window which could easily allow warmer weather to interfere with the temperature regulation (the episode's opening scene states that Gotham is in the midst of the hottest August on record). (00:21:00)
Correction: A single small window even in an area of high heat would not be able to interfere that much in a sub-freezing room with a dedicated hyper-cooling system.
Correction: Clayface wasn't faking losing control of his abilities. He really was losing control. When Clayface saw all the characters he played over the years as Matt Hagen, he began turning into each of them involuntarily but, because there was too many of them, he became overwhelmed and couldn't stop transforming. He even begs Batman to shut off the screens. Https://www.youtube.com/watch?v=K4W8Wp6SzdM.