how well does sheet dps correlate with damage output?
are there occasions that one has high sheet dps but low damage output (with the same skillset)

same for toughness v.s. survival, and sheet heal v.s real heal

Sheet dps is broken, Diablo progress proves that since skill and ele dmg aren't calculated in sheet dps. And blizzard is going to revamp toughness and healing in an upcoming patch, so I'd assume those are broken too.

toughness is too health pool biased, it's been proved that by going higher resists, you can get a higher equivalent health pool while lowering your "toughness". It also doesn't factor the fact that having high res, low health, makes healing way more valuable.

This. A -5% toughness item can actually give you more practical toughness (ar > vit).

As for damage, it's alright for a rough estimate but you have to check for +ele gear

As they have all said it's not correct, but also choice of skills can effect damage night and day.

My "sheet dps" ingame is 950k but Diablo progress shows 2.1 million.

Both are wrong, my primary crits for 3-4 million and spender crits for 20-32 million.

diabloprogress is bad too +ability dmg not counting

True but a bit better to check if items are helping otherwise

I am pretty certain that these concepts are meant to function as simplifications.
They are meant to be something like "crude guidelines", I think.
AS, for example, will get you alot more sheet dps, but what it doesn't show is how long you can maintain your resources at that AS.

You should go with your guts instead.

Also the skills you use make quite a difference.

You can't really know how the other person does in a team unless you play with him, pretty much.

your dps stat is your approximate auto attack dps. granted this does not take into account ele damage or skill damage. But if you know these stats you can get an approximate. Your damage is calculated multiplicatively by each modifier, so if we simply start with your dps which has already been calculated via (wpn dmg x IAS x (CC x CHD) = Sheet DPS or sDPS)

Lets say you have 1mil sheet dps(for simplicity). this means if you don't put a skill on your left click your basic auto attacks will result in about 1 millioin damage per second.
Now lets put a skill there. How about a 200% weapon damage ability. This skill's dps will be 200% of your sheet dps when used, so ~2mil. (sDPS x Skill Weapon%)
Lets make a decent assumption that you have some elemental gear, how about 50% fire and this ability is a 200% weapon damage fire skill. This ability does ~3mil dps. (sDPS x Skill Weapon% x +Ele%)
Now lets make another assumption that you have some +Skill% damage, 30% seems reasonable. This skill now does ~3.9mil dps (sDPS x Skill Weapon% x +Ele Dmg% x +Skill Dmg%)

The numbers: sDPS = 1,000,000 Skill Weapon% = 200% of total or 2 + Elemental Damage% = +50% or 150% of total or 1.5 +Skill Damage% = 30% or 130% of total or 1.3
Skill DPS = 1,000,000 x 2 x 1.5 x 1.3 = 3,900,000 or 3.9mil DPS

So, while your sDPS shows you 1million, using some simple math you can come to a reasonable conclusion that the skill you are using with element and skill damage factored in, you are doing 3.9 million DPS while using that skill.
So in a way, yes, the dps calculation accurate if you know how to use it properly.