In a word, the answer to that question would probably be "Decently". The first episode is pretty good at showing exactly how the rest of the season will play out. It starts out on a high note with some typical Shin-humor, but quickly begins to fluctuate between the familiar humor and vulgarity.
I'll step back a bit and give some perspective on the show and it's situation. Shin Chan is an episodic comedy series that focuses on the escapades of Shin Nohara, his friends, and his family. Shin himself is a crass 5 year-old child that lives life the way that he wants to. There's no plot or advancing timeline in Shin Chan, it's entirely a vehicle for comedy. Domestically, the show is only available dubbed, and was airing on Adult Swim up until a few years ago.
The departure from Adult Swim has definitely had an effect on Shin Chan, as the vulgar and political jokes have been turned up several notches. The effects can often be pretty painful as a viewer. It's obvious that the writers are trying to push the envelope as far as they can, making quite a few of the jokes groan-worthy. Georgie's political prattle seems worse than ever; longer scenes are nausea-inducing no matter your position in the political playground. Skits that focus entirely, explicitly, and blatantly on sex and drugs make me wonder if the writers are just not clever enough to support better attempts at humor, and instead rely on trying to shock the audience with "edgy" humor.
I'd like to stress here that I'm no prude; I find that my tolerance for the vulgar aspects of anime is rather high. What I have issues with here isn't exactly "edgy" content, it's the fact that so many of the skits now seem to rely on it.
Let's take a look at an example. In one scene, Shin and his friends are trying to get strangers to adopt a stray cat. The deft humor throughout the scene is built upon the double entendre behind cat and pussy. It's was worth a chuckle once, but hearing it over and over again throughout the scene just proves that the writers couldn't think of any other applicable jokes, but decided it was good enough to chuck in. The overall result is something that I can recall hearing over and over again in from other students in the 7th grade.
Luckily, these awkward attempts at humor are usually confined to certain characters. Georgie's political jokes, Bitzi's "Brown-brown" addiction and sexual fling with Hiro's dad, Maso's gay jokes, these are the characters and jokes that make me want to find something else to watch. Other characters are consistently great, and have avoided much of the writer's poor taste. Shin and Hiro are as hilarious as ever. It's almost as if the creativity that other characters lack has been funneled into Boo, who seems to be at his all-time best. Some of his one-liners kill me, and they stand out as some of my favorite jokes of the season.
If I've tried to make anything clear here, it's that Shin Chan Season 3 is a mixed bag. Some of the humor is great, some of it falls short, and some of it was pushed so far that it had no chance of coming close to the Shin Chan that I love. If you're a fan of the show and are looking for more Shin Chan action, go ahead and get Season 3. You'll get some great laughs out of it, for sure. While Shin Chan is not at it's best in Season 3, I still think that it is at least worthy of watching, and perhaps purchasing when the price is right.