So, I've played with this update for some time and here're my recommendations.
1. I got Bat Bat when it was meant to be obtained (very early-game) and it is pretty good for that period of the game. However, it soon gets outclassed by other melee weapons (like an Ice Blade, Starfury, or Storm Spear) which definitely shouldn't be the case for such a rare item. I agree with others that its healing capabilities should be buffed to make it a good option. After all, it's a true melee weapon with not the best stats, so healing with it consistently would still be a bit challenging. (I know that I haven't said anything new, but I think that my feedback is still a bit useful).
2. I like your idea of Tentacle Spike being a good, but be hard to get melee weapon (like with Ancient Shadow Armor), however, I don't think that Light's Bane is a good comparison. Shadow armor is a post-EoW armor, so it's quite powerful compared to pre-EoW armors. Light's Bane, on the other hand, is a post-EoC sword (and can actually be obtained pre-boss if you want to mine Demonite), so grinding for a weapon with around the same stats won't matter much. I think that you should compare Tentacle spike to Blade of Grass to balance it correctly (It definitely should not be identical to it, but it's a more reasonable comparison). Also, I don't really think, that it should be changed much from it's DST alternative. Yeah, it can be a bit boring, but I think that it staying canonically-accurate matters more. (It may have a fun gimmick, but definitely not something like shooting projectiles).
3. I do agree that Froggle Bunwich needs a nerf. And I agree with CrabBar's idea of changing Froggle's recipe. It does need to require something other than Frogs to make it more different to Sauteed Frog Legs.
4. Abigail's Ghost used to be a bit too powerful in some cases (mainly in Hardmode when she was a good alternative to Blade Staff or Sanguine Staff when paired with Firecracker), but now (even though I haven't tested it yet) it should be fine.
5. I think that making Chester available in pre-hardmode makes Money Trough much less useful. I would actually ask to move him in early Hardmode to make him a bit more balanced (it can drop from snow biome enemies in early hardmode, maybe from Ice Golem). And also I was very disappointed when I found out that Chester is a pet. It means that you have to sacrifice your favourite pet to use him. And in this scenario I'll prefer to use a Money Trough since using the pet I want is important fir me (but a lot of people won't care since they put effectiveness above cosmetics). I agree with J Bame's idea of making him a light pet. Then you'll have to switch from one '"utility pet" to another. And on "The Constant" seed where darkness is dangerous, this decision will be even more impactful. Although I am a bit afraid, that this change won't make Money Trough farming much more useful...
6. And here's something I don't think anyone mentioned here (although it's not very fitting for the title of this thread, but I think it's still a suitable place for it). I'm not a fan of Deerclops not despawning mechanic. It allows you to cheese him (it may take some time, but you can potentially defeat him pre-boss by running to the snow biome over and over again) and get his items. As far as I know, he doesn't despawn in Don't Starve, but this mechanic doesn't fit Terraria that much. And since you're against cheesing bosses (as you've fixed a lot of various cheesing methods in 1.4), I think you should make him despawn when every player is killed. Right now this boss is in a good position of being a pre-hardmode Duke Fishron (you can fight him early, but it requires you to be skilled), but the challenge is nearly ruined because of him not despawning.
These issues aside, this update is amazing! Good job Re-Logic!