Revealing mistake: When Kramer is getting slammed with his new super-powered shower head at the very end of the episode, it's blatantly obvious that the water is barely touching him - he's standing right next to it.
Other mistake: While Jerry is looking out the window, to his right, there is a Yankees baseball cap on top of his mini basketball hoop, above his computer monitor. Jerry in real life is a Mets fan, and he alluded to being a Mets fan on the show as well (taping a Mets game, wearing or showing Mets paraphernalia). In no universe would a Mets fan have a Yankees cap on display and vice versa. This was before George got the job at the Yankees so that can't explain it. Was it just bad set design and props? (00:14:22 - 00:15:30)
Suggested correction: There's a Yankee hat in many previous episodes. It's never mentioned where it came from, but it could be a gift or signed or hold significant value to Jerry as opposed to him buying himself a Yankees hat to put on display. And that's assuming Jerry in the show is such a Mets fan that he wouldn't like the Yankees as well.
Factual error: With the size of that red ball (approximately 2.5 foot diameter) and the density of oil (approximately 60 lb/ft^3), the giant ball of oil would weigh 491 pounds. This would be impossible for Kramer and Darren to lift out of the window and would definitely kill anyone it beaned.