I thought the excuse for not going back to the crucifixion with time travel was practical enough even if there are real world considerations of why not to do such a story.
Although it would've been nice if Rip had given some other examples of historical events too important to change, such as the life of Moses, Muhammad, the Buddha, Guru Nanak, etc. As it was, it came off as kind of Christian-centric. Heck, the whole Spear of Destiny premise pretty much implied that Christianity is the one correct religion in the Arrowverse -- although Vixen's Anansi Totem proves that at least one other pantheon is real therein.
I can't remember if it they showed it before, it seemed familar, but I like that the LoD headquarters looked like the one from the Superfriends.
Well, it wasn't really their HQ here; rather, it was the site of the reactor Thawne had Stein and Jax build (so, no, we haven't seen it before). Thawne's HQ was STAR Labs, which makes sense, because he was the one who built it when he was impersonating Harrison Wells. Darhk's HQ was City Hall in Star City (although it should've still been Starling City, since the name change was Ray Palmer's idea and he was a janitor here). I'd guess Malcolm's HQ was the Merlyn Global Group building in Star City, or maybe Nanda Parbat, or both. Snart's HQ... I dunno, maybe that dive bar he hung out in on
The Flash.
In seriousness, I tend to think of the shows working in near-time with each other so they're in the proximity of each other for the most part but not necessarily that day or week of unless a specific crossover requires it. If Supergirl is having a coffee with Barry on his Earth in The Flash it could be from any relatively recent time not specifically in the middle of fighting off an alien invasion in the current episode and so on. I'm not even sure if LoT is currently in any one date anymore.
The other shows are generally roughly in sync, except when they clearly aren't. But since LoT is so rarely in the present day, it doesn't even make sense to treat it as simultaneous. I mean, how can WWI or the Old West or Camelot or the far future be considered simultaneous with the present? You can talk about how much time has passed subjectively for the Legends, but that has no relationship to the passage of time in the normal world.
It's pretty clear, though, that the time flow between Earth-1 and Earth-38 doesn't quite line up, or at least that breaches between the worlds have some temporal uncertainty. After all, Barry and Cisco recruited Kara to help with the Dominators at the end of "Medusa," which was set on and just after Thanksgiving, but later references in both
The Flash and
Arrow date the Dominator invasion to the week before Christmas. So the two sides of Cisco's breach were displaced from each other in time by about three weeks. Which, coincidentally, is the same as the gap between the airdates of "Worlds Finest" (when the Flash first came to National City) and "Versus Zoom" (showing the Earth-1 side of that crossover). And of course the Flash was gone for mere seconds on Earth-1 while a couple of days elapsed on Earth-38, so clearly there's some timey-wimeyness going on.