It seems like Hayate no Gotoku is getting shorter and shorter seasons. The first was 50ish episodes, the second was 20+ and the third is only 13. The fourth is probably just going to be a bunch of OVAs -_-
Right, so what is Season 3 of Hayate no Gotoku about? Well, it's mostly about the backstory of Nagi's parents, with a new character claiming to be Nagi's half-sister showing up. It's also said to take place several months ahead of the current manga continuity, which really bummed a lot of readers out. Mostly because the manga had a much better storyline going on but judging by the state of the anime; it'll be status quo again -_-
The anime is fairly weird in the sense it's supposed to take place in the future but it also borrows a lot of one-shot stories from waaay back in the manga's past and then animates them. This leads to a bit of continuity discontinuity. Although to be honest, I'm not that huge a fan of the animes setting since I don't really care about Nagi and I'm not that interested in the overarching backstory about the kings jewels either.
To be honest, I can not understand why on earth they chose to animate this particular arc. Why the future? That kind of kills a lot of the suspense for readers of the manga since now we know WHAT'S going to happen (spoiler; NOTHING AT ALL) and secondly, there are a lot of better arcs to animate.
Seriously, what about the Athena arc? What? That's not even going to be animated??? One of the MOST important arcs in the manga, along with a shitload of hints and revelations about Hayate's backstory and we're skipping it??!?!
And let's not even mention the elephant in the room. What about Ruka?? What's up with her missing from the movie and the anime? She was a popular character introduced in the last 80 chapters and there's NOTHING about her at all? She just appears in CVs on TV and provides idle commentary? What a WASTE!
Overall, Hayate S3 wasn't as good as the first 2 seasons for several reasons. It skipped too many important arcs, didn't introduce enough of the popular characters whose arc we would actually like to see ANIMATED and also, not enough Hinagiku.