Unrealistic Thing #1 is obviously the discovery of his mom. It seems like a stretch on so many levels. Sympathy towards dragons seems like an unlikely genetic trait, so the idea that she would turn out to be a dragon friend/expert too without any memetic connection between the two of them seems a little odd. Not to mention of course the getting kidnapped by dragons thing and then being rediscovered 20 years later.
Also, in the first movie Hiccup's dad says that his helmet is made out of half of Hiccup's mom's breastplate, and gives Hiccup a helmet made out of the other half. Just to be clear, i really like Hiccup's mom's character design, but i don't quite see how her breastplate could make a decent helmet for anyone.
I do have to say that i appreciate there wasn't a lot of drama of the kind Hiccup's mom seemed to expect when his dad found them. Although it seems rather cruel of the writers to have them find each other only for him to get killed a couple hours later.
Unrealistic Thing #2 is Toothless' spine ridge flap things. There are several issues with this.
First, how does his mom know about them? She said that Toothless might be the last Nightfury in existence (though you can bet that if this movies does well there are decent odds that a colony of Nightfuries will be found in the third movie =) The implication is that she hasn't seen any others, or that she has good reason to suspect that any she's seen in the past are dead now. If there was a Nightfury at her colony (the only situation in which she'd be likely to get close enough to discover this) then what happened to it?
Next, how does a species evolve with a feature that seems to be provide a significant advantage, but that can't actually be used until a third party comes along and does some kind chiropractic routine on your back? The idea that he would have no idea he had the flap things or have any instincts to do whatever is necessary to get them to pop out is bizarre.
And the reason they become relevant, supposedly, is that Hiccup keeps doing his wingsuit thing, keeps unexpectedly encountering obstacles, at which point Toothless tries to save him, but always does so in a last-minute kind of half-assed manner. (Although that sounds like it's putting the blame on Toothless, which isn't really fair.) When that happens with his mom there, she does the thing to make the flaps out, and says something along the lines of "this will allow him to make sharp turns."
I'm not sure if it's outright stated as such, but that certainly implies that the reason Toothless failed to save him in an elegant manner was because of his failure to make sharp turns. Except that A: it's not readily apparent that sharp turns would really have helped in any of the instances. Then at the end of the movie when they pull off the maneuver successfully it doesn't seem to involve any sharp turns. And finally, we've seen Toothless perform plenty of maneuvers before this that i personally would qualify as sharp turns, and he doesn't seem to be noticeably more agile after popping out the flaps.
I do appreciate that they didn't feel the need to insert some kind of relationship drama between Hiccup and Astrid (though i was slightly worried about that before it was revealed that the other dragon rider was his mom.) I hate it when they feel the need to rehash the established relationship in every movie. I'm not so sure how i feel about the whole sub-plot with the female twin. Sure, it's mostly treated as a joke, but this seems a bit less like Belligerent Sexual Tension and a bit more like "just ignore the fact that the girl has stated she's not interested in you, just keep following her around and harassing her and if you find a way to save her life she'll instantly fall in love with you."
I did manage to predict how the movie was going to end, which wasn't that hard given that i'd been warned it's a pretty stereotypical hero's journey. However given that i didn't have a stopwatch handy or any idea of exactly how long the movie was, i thought Toothless was going to have his showdown with Alpha #2 right before the point where he actually ended up killing Hiccup's dad instead. Oops.
I'm a bit curious about how badguy bloodyfist tamed Alpha #2 in the first place. It didn't seem like the stick wavey thing ought to have been enough by itself. The one time it was showed off he had to shield himself from a flame attack from the dragon in question using his dragonhide cloak before he was able to pull off the intimidation thing. The kind of damage an alpha dragon does can't be shrugged off so easily however.