In uniform, shared light levels, vision penalties due to darkness work fine, intuitively, and exactly as written (no surprises). The deeper the darkness, the more trouble you have seeing, hitting things, and protecting yourself.

This, however, isn't the case you're asking about.

Mixed lighting conditions

Let's stick with RAW to analyse this situation of two people in different lighting conditions. The results are almost entirely the same whether whether Aspartame is in magical darkness or the (possibly very dark) shadow of an oak tree. The results are going to be weird.

• While Aspartame is in dim light, he has concealment.
  • Xylitol gets a 20% miss chance firing upon Aspartame, because Aspartame has concealment.
  • Aspartame can't see clearly, because he's in dim light. (Even though Xylitol is standing right there in bright light.) He either fires upon Xylitol without difficulty, or suffers the same 20% miss chance for firing through squares that grant concealment.

• While Aspartame is in darkness, he is blinded.

  • Xylitol has a 20% miss chance still, if we interpret Aspartame as still having dim light concealment. Natural darkness doesn't provide concealmnet explicitly, just blinds people in it.

    • People in the Darkness spell's darkness, however, get total concealment according to that spell. Since Aspartame has total concealment, Xylitol has a 50% miss chance. (This is the only difference made by the spell. Aspartame is still blinded either way, because it is dark.)
  • Aspartame, who is standing in darkness, can't see anything and has a 50% miss chance firing on Xylitol who's in daylight.
  • Aspartame takes all the AC and sensory penalties for dealing with anything because standing in darkness has made him blind.

These results are pretty counter-intuitive. In real life, the rogue sneaking through the shadows has an advantage on everyone else, and you've probably handled it as such — the rogue themselves isn't blinded by being in the shadows, but they are in Pathfinder!

Pathfinder's vision penalties are counter-intuitive and weird because they don't correctly model vision as we know it: they give you trouble depending on the light level you're standing in, instead of giving you trouble based on the light level of the thing you're looking at. In reality I don't have trouble reading things in the dark because I'm in the dark, I have trouble because those things are.

Like I said though, they work fine when people are sharing the same light levels. They just weren't written with differing lighting conditions in mind and don't handle them well. The sacred RAW should be burned in this case upon the altar of This Could Have Been Written Better For These Cases. Rules are worth the results they produce, and here the results they produce are kinda dumb. Those who wish to apply it exactly because those are the rules can go ahead and suffer the headaches.

Drawing sense out of the ashes.

Pathfinder should probably just be modelling how things really work: darkness affects you based on what you're looking at, not what light level you're in. Accordingly, I'm making a recommendation that in mixed light levels, the RAW be interpreted for what it was probably intended to do — which just requires a small adjustment of the original RAW:

• Dim light: Being in dim light doesn't make you have trouble seeing, but looking at things that are in dim light means you have trouble seeing those things. Past that though the RAW works fine: things in dim light have concealment and you have a 20% miss chance against them.
• Darkness: Being in darkness doesn't make you blind or suffer penalties. However, you are considered blinded for the purposes of observing or interacting with anything that is in the dark. You have a 50% miss chance against those things in combat, you have penalties to AC and perception versus things in darkness, and so on.
  • Alternately, stick with the Darkness spell's function, and just grant things in darkness total concealment and forget about blindness.

Wyrmwood brings up in comments that due to firing through concealment, firing past/through dim light introduces a 20% miss chance. This causes sense-making problems if you're on a long archery range, and a tall tree off to the side is casting a shadow across part of the middle of the range: those rules assert your target dummy now has concealment, despite still being in the bright daylight. These rules work fine for actual obstructions like black smoke, but not for light. I suggest that for the purposes of firing through concealment, don't count dim or dark squares — just count what it is you're targeting.

That produces these results, which are probably actually intuitive:

• While Aspartame is in dim light:
  • Aspartame is considered as having concealment from Xylitol. Xylitol has trouble seeing him, and has a 20% miss chance.
  • Aspartame fires without difficulty, because Xylitol is in bright daylight and clearly visible.
• When Aspartame is in darkness:
  • Xylitol is considered as being blinded for the purposes of trying to observe Aspartame. He has a 50% miss chance trying to attack Aspartame.
  • Aspartame still fires without difficulty, because Xylitol is in bright daylight and clearly visible.
  • Xylitol has all the defensive and sensory penalties for the purposes of any interaction between himself and Aspartame, because he can't see what Aspartame is doing at all.

We get these results, again, whether the dim light or darkness is due to magic or the shade of an oak tree.

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).