While talking to Brody, Chloe removes sunglasses she wasn't wearing.
The boat stops moving as soon as Lucifer snaps the rope. Momentum, the motion of the water, and the lack of mooring should have kept it heading out to sea for a few yards at least.
The title on the newspaper article on "preacher" Williams's death says he "dies" at Lux. However, as from the attached picture he was clearly murdered, a real newspaper would have used the more accurate and attention-grabbing terms "killed" or "murdered" in the header. One of the article headers on Pierce says he "is eulogized 'One of the Best'." Newspaper headings generally avoid "is" phrasing both to create immediacy and save space - it would have been written without the phrase "is eulogized".
While Lucifer may be invulnerable if Chloe is not present, his clothes aren't. Yet when he emerges from the gas explosion of The Cabin his clothes appear to be intact, not even singed. One would expect him to emerge either naked or with his clothing afire.