Ahh, so no casting a second spell it looks like

I just wish I could use it on multiple targets at a higher level.

Also, when it says "Attack (one weapon attack only)" is it saying that you can only use one attack action, however many multiple-attacks it is but not an extra off-hand attack? Or only that you get a single slash or stabbing or bludgeoning?

After a bunch of scouring, it looks like the official word is that it's a brand new attack action, but it can't trigger 'Extra Attack' abilities like the fighter's/monks where you'd get more than one strike.They're the kind that are usually phrased like "... you can attack twice, instead of once, whenever you take the Attack action on your turn. "

However, it does trigger abilities like Horde Breaker or Dread Ambusher, that give you an additional attack when an attack action is used. These are usually phrased like "...you can make one additional weapon attack" or "...you can make another attack" etc.

Hope that helps.

I Think with that One Sourcerer Thing you can keep  it on 2 targets if you spend the points

You can cast it on two targets if you are sorcerer and have twinned spell option in you metamagic ability.

Twinned Spell

When you cast a spell that targets only one creature and doesn’t have a range of self, you can spend a number of sorcery points equal to the spell’s level to target a second creature in range with the same spell (1 sorcery point if the spell is a cantrip).

To be eligible, a spell must be incapable of targeting more than one creature at the spell’s current level. For example, magic missile and scorching ray aren’t eligible, but ray of frost and chromatic orb are.

Does the 'advantage on Dexterity saving throws' include the 'dexterity check to determine their place in the initiative order'? PHB pg. 189

It strikes me as a weird oversight if not

Surely this is one of the most important instances where acting more quickly than others would be of most value?

Quote from LichwayEd >>

Does the 'advantage on Dexterity saving throws' include the 'dexterity check to determine their place in the initiative order'? PHB pg. 189

It strikes me as a weird oversight if not

Surely this is one of the most important instances where acting more quickly than others would be of most value?

 That is a Dex check not a saving throw

How do you track this if someone else casts it on you. If you're a barbarian or monk that usually doesn't use such spells, but a wizard casts it on you or you use an item, how do you add it to your character to track it?

I was going to say add it as a condition hasted but that doesn't exist so the answer is poorly

This is where having the spell caster write out the effects of their spells comes in handy. My bard casted spells like this a lot and would write up cards to hand to players who they cast it on. It worked pretty well! Hopefully dnd beyond adds something later on to keep track on their website.

Quote from Elunedra >>

I was going to say add it as a condition hasted but that doesn't exist so the answer is poorly

I read that this lets you sneak attack again with the extra attack on a forum, but i can't see where or why it would let you do that.

According to Sage Advice you can only get one Sneak Attack per turn. You get an extra action on your turn, which is the same turn, so only one sneak attack.

I have druid with some level 3 wizard. Can I cast haste on myself and then use wild shape? Would the haste work?

Quote from Mares4201 >>

I have druid with some level 3 wizard. Can I cast haste on myself and then use wild shape? Would the haste work?

Well haste is a level 3 spell meaning you need 5 levels in wizard to be able to cast it as explained on the wizard table in the PHB.  However, assuming you can cast haste, you still wouldn't be able to use another action to do anything except exactly what it says you can do on that turn.

it gains an additional action on each of its turns. That action can be used only to take the Attack (one weapon attack only), Dash, Disengage, Hide, or Use an Object action.

What you want to do seems to be cast haste on yourself, turn into a wild shape animal, then attack.  You can do this but only if you are a circle of the moon druid.   You'll use your normal action to cast haste, your bonus action to turn into a bear or whatever, then use your haste action to attack.  You can concentrate on a spell while in wild shape form so there is no issue there.  What I am not sure about is what happens when it's your next turn.  If your wild shape has the multi-attack feature, does it use all of its attacks twice?  Just one?  Not sure how this should be ruled.  Probably just one extra attack but honestly this is a weird case.

gotta go fast

Artificers get this. "I invented a 30 foot syringe, for all your self-medicating needs!"

Isnt dread ambusher first attack only?

Quote from Stinkingyeti >>

I read that this lets you sneak attack again with the extra attack on a forum, but i can't see where or why it would let you do that.

 You need to be a bit tricky. Attack with the New Action from Haste, get a sneak Attack. Use Your normal Action to ready an Action, attacking the opponent again at some point before they act- since it's Not Your turn by then anymore, "Once a turn" is statisfied and you can sneak Attack again. 

Ooh, this is good. You're some kind of genius.