Caveat: I don't think this is incredibly clear from the wording of the spell, so my answer will be subject to some semantic parsing.
No, that errata does not impact the effect of the Darkness spell.
The fact that "darkness" as opposed to "the effects of the Darkness spell" is listed as an example of a heavily-obscured area and that the spell description doesn't describe it as creating "a heavily obscured area" means that errata is kind of a red herring in this case.
The spell description says that a creature with darkvision can't see through it (which requires the logical leap that creatures without darkvision also can't see through it :) ), which means someone in the area of effect can't see out, since that would require seeing through some portion of the darkness.
A more grody scientific explanation would say that since "nonmagical light can't illuminate it," you can't see something unless light bounces off that thing and hits your eyes, and light that does do that would potentially be illuminating something in the darkness, so...no on that front as well (though if your game gets to the point of debating the nature of light itself, you might want to call it a day already).
I see nothing there that implies it is a barrier to vision, just an active and utter absence of illumination.
You are quite right - there is nothing in the spell that says it blocks vision, just that the area is in Darkness.
However, a strict reading of normal darkness means you can't see through that (PHB p.183):
Darkness creates a heavily obscured area. Characters face darkness outdoors at night (even most moonlit nights), within the confines of an unlit dungeon or a
subterranean vault, or in an area of magical darkness.
And a Heavily Obscured area is (PHB p.183):
A heavily obscured area—such as darkness, opaque fog, or dense foliage—blocks vision entirely. A creature in a heavily obscured area effectively suffers from the blinded condition (see appendix A).
Which has been erratad as:
A heavily obscured area doesn’t blind you, but you are effectively blinded when you try to see something obscured by it.
So, darkness (magical or otherwise) creates a heavily obscured area. A heavily obscured area "blocks vision entirely".
Now, while it is clear what this means for "opaque fog, or dense foliage" is simple and straightforward - you can't see into this stuff and you can't see through it to stuff on the other side of it.
Applying this to darkness, however, seems to result in nonsense because, in the real world, darkness isn't a thing. In the real world darkness is the absence of light hitting your eyes from a certain direction. This can be because of an actual absence of light (underground) or because, even though the region is full of light none of it is coming your way (space). But this isn't the real world, is it?
So you have 3 options:
- Darkness works just like it says in the book - you cannot see into it or through it. This would be really cool for a gothic horror campaign even though it would make navigating at night ridiculously hard.
- Darkness (magical or not) works as it does in the real world - you can't see into it but you can see through it to illuminated areas beyond. I think this is what the rules intended even though they and the errata were poorly drafted.
- Normal darkness works like 2. Magical darkness works like 1. There is no support for this in the Darkness spell description but this is how it worked in prior editions.
Its your world - make it fun.
Best Answer
An invisible creature's light source still emits light
Most arguments against the light source still emitting light seem to argue based on the real world's understanding of electromagnetism.
D&D is neither the real world, nor a physics simulator. The rules only do what they say they do.
For all we know, the worlds of D&D follow the emission theory of vision:
Using this theory, it could be argued that it is perfectly reasonable for the creature (and light source) to be unseeable.
Example argument: The invisibility effect prevents "eye" rays from hitting the invisible target (and instead passes through them), but the "source" rays from the light source would not be affected, and so would still shine normally on the surroundings.
However, D&D is not a physics engine for discarded theories either.
As such, we only have the "rules only do what they say they do" to determine what happens.
What the rules say
A bullseye lantern description states:
If a creature is invisible, there is a description in the conditions for what that means.
However, we are looking at an object being carried being invisible (as the rules for a creature were unenlightening -- no pun intended). I couldn't find any specific rules on what an object being invisible meant so we'll fallback to the English definition of invisible:
The lantern is incapable of being seen. Baring any other rules that I've overlooked being relevant, that's all being invisible does for an object. It does NOT prevent light being cast around the object.
Jeremy Crawford's tweet
From this, we reach the same conclusion that Jeremy Crawford provided.
The invisible creature can see with its own light source
You also asked:
So, we know that light is cast, can you as an invisible creature see it?
According to the rules for Vision and Light:
Again, given a lack of any other rules to contradict this, yes, the invisible creature can see the light cast by a light source they are carrying. (Similar rules for the dim light cast, but this is far enough down the rabbit hole of rules.)
Additional effects are defined by the DM
Rules only do what they say they do, but the DM is free to add any additional effects they desire.
Personally, I find the description that Jeremy Crawford used to be quite amusing, and
believe my players would as wellmy players did as well.(A year an a half after writing this answer, this actually came up in one of my games, and my players used minor illusion to make "ghost sounds" and enhance the "spooky" nature of the light being held by an invisible character.)
However, each DM can rule as they see fit, but they should be consistent from one instance to the next, so the players can plan and play their characters in a consistent world.