Dany freeing the slaves in Astapor was definitely more strategic than "Dragons, go". Setting up the deal and then double crossing the guy IS one of the older tricks in the book, but still, it was a pretty smart move. I mean, dragons or not, I don't think Hodor would've pulled it off. Or Joffrey or Viserys.
Actually Joffrey or Viserys would have done exactly the same as Dany has done to the slaver guy. It was just very convenient that he didn't even question it when he made the deal, just as it was convenient that Darios decided he liked her better than his two captains and was able to overcome those two as well.
My main problem with Dany is that her character progression was over in season 1. Her arc in S1 was great, you had her slowly assuming control as Khaleesi and being able to free herself from Viserys. I mean even her relationship with Drogo was very nicely portrayed. You could say it was still very convenient to be able to run into the one Khal who actually decided to take an interest in his woman and not just fuck her but there was a case to be made that she actually worked for it.
But then Dany stepped into the fire and everything changed.
You can see at the start of S2 that she is still very much like at the end of S1, which is great. She is going through some tough times and trying to keep her people alive. But once they reach Quarth she immediatelly becomes unlikeable. Her conversation with the Spice King and the fact that she overplayed her hand should have taught her that while she does have dragons she really doesn't have that much power yet. Xaro saved her for plot-related reasons and that was ok. But she pretty much continued on with her acting as a powerful Queen for the rest of the season, even when her dragons were taken away from her. Actually the moment in S2 finale when she is reunited with her dragons actually captures the 2 seasons perfectly.At the start you see the caring Dany who talks to Drogo but then then you see her tied up for 5 seconds and she easily gets out of that situation with a smug look because 'lol Dragons'.
In Season 3 Dany seems to continue on with this path. She seems a bit wiser (not revealing to the slaver that she spoke Valarian), though there was that moment when she shut Jorrah and Ser Barristan as if she knew better, but once she gets into position of advantage when she takes over the Unsullied she reverts back to simply using the dragons to get out of every situation. Her threats to Yunkai are the same, she continues on being smug simply because she has the dragons. Then finally in this episode we finally see a threat to her and hilariously it is like the slaver said, all she does is flash her tits and gets her way.
The problem here is that Dany is acting all high and mighty despite not really achieving anything nor actually resolving any difficult situation herself. Things just sort of fall to her and that's it. She is not at all comparable to the other big players in Westeros. I mean compare Robb to her, he is has won every battle, true. So you could say things are working out conveniently for him too. But yet he has been faced with difficult situations like beheading the Karstark lord or losing Winterfell. All the while he doesn't at all act like a smug little child when negotiating or around his advisors.
I would say that this can be down 2 factors, Dany being a true Targaryan and they are cruel conquerers who think too much of themselves by default or Emilia Clark's acting.
2 scenes to illustrate the point I'm trying to make can be take from the last 2 episodes Dany was in. When talking with the Yunkai lord Dany is referred to as 'Daenerys Targareay, Queen of the Andals and First Men, Khaleesi of the Dhotraki and the Mother of Dragons'. Now she is not the Queen of Andals or the First Men. Actually the only two Andals she's commanding are Jorrah and Ser Barristan. All the other don't even know she's alive and I very much doubt they'd actually welcome another Targaryan returing. She's also not the Khaleesi of the Dhotraki as the Khalasaar has moved on to find a new Khal and he will have his own Khaleesi. I now this is very minor and a nitpicking argument but it underscores how highly Dany is thinking of herself. Everyone else in the series calling himself a king actually seems to have done something to deserve it: Joeffry is, as far as people know, the heir to Robert, Stannis is the heir if Ned's accusations are true, Robb is in open rebellion with the South and in fact the South no longer controls the lands where Robb is King, Balon Greyjoy has done the same as Robb but with the Iron Islands, Mance has united the Wildlings.
Second scene is from this episode where she is being bathed by her servant. It's just such a jarring scene when you watch it and compare it to the stuff Robb, Tywin, Stannis, Jon or Arya are doing. Danny seems to be living off in luxury which she has acquired simply thanks to the dragons. It just strikes me as too much of a wanna be queen scene, where really Dany has done nothing to deserve that status yet.
