This description omits the very important third sentence: "The spell ends for a target that attacks or casts a spell." We just almost lost a party member because we didn't know that.

I think you're mistaking this page for the 2nd level spell "Invisibility".  This is "Greater Invisibility", a 4th level spell, and the ability to attack and cast spells while remaining invisible is the "greater" part (they don't seem to represent the change in duration in the title).

A ha! Indeed, between myself and my DM we were reading two different entries. Thanks for the clarification.

They should probably add in "Additionally, for the duration, you can take actions that don't break concentration without the spell ending" or something 

Quote from Harden865 >>

They should probably add in "Additionally, for the duration, you can take actions that don't break concentration without the spell ending" or something 

That would be excessive at best and misleading at worst. The spell is pretty explicit as is. The target creature is invisible until the spell ends. The spell requires concentration and has a maximum duration of 1 minute. If they added that additional clause then it would imply that other spells with concentration requirements didn't allow the target/caster (you're unclear who it should apply to or if you assume they are the same creature) to take actions that don't break concentration without ending the spell. Otherwise the spell is just re-explaining how concentration works.
5e is set up to use general rules and then provides features and spells that break, circumvent or change the rules in specific ways. Concentration is a general rule used by many spells and spell-like features. It is explained once and then referenced.
I hope this didn't come across as harsh and that my rambling made sense.

Why is this greater then plain old invisibility spell? This one only lasts a minute.

You can attack/cast spells without losing the invisibility. If you’re just scouting or sneaking around aka not in battle. Just use regular invisibility.

Oh, cool.

This doesn't apply to greater

This spell feels like it could do with one of those sidebars, like we've seen in various UA documents. Something to the effect of "Many effects that grant invisibility are broken if the recipient attacks or casts a spell. Note that greater invisibility has no such restriction. That's not a property of the Invisible condition, it's specific to those other effects." It's technically unnecessary - spells do what they say they do, yada yada - but enough people are confused about it that it's probably worth putting in there.

Does up casting this cause more targets ? Feel like I have seen it used that way or somthing similar 

The Level 2 Invisibility spell allows multiple targets to become invisible by casting the spell at higher, levels.

This spell allows only a single target "You or a creature you touch" and has no casting bonus at higher levels.

As mentioned before, it has no upcasting bonus.

However, a sorcerer using the twinned spell metamagic could affect two targets at once.

More of a hide a party member during combat utility than a scouting utility.

Casting words are:

Ementitus Librarium Invalidius

This is fun to cast on PCs by enemies with true sight or see invisibility. That way they can't be targeted by the healer or anyone who would buff them. 

ohhhhh, I like that.  That would require a melee attack roll though is it's an unwilling target, one could safely assume they won't just stand still to be touched.  A miss would waste the casting......pretty big risk.  Would be great fun if it worked though

Fair, but familiars can help with the risk there, at least for getting into range. It's also fun to give BBEG monsters the ability to cast Greater Invisibility at range as an offensive spell like ability. 

If my BBEG gnome was being carried by his Huge Ally, could the gnome cast Greater Invisibility on the ally and be invisible himself as long as he is being carried?

Or, the Gnome is just bobbing up and down in mid air. That would be hilarious