This show truly proves that you can make anything interesting if you're talented enough. I can't imagine anyone other than the people who worked on this make a story about competitive bread making as over-the-top and intense as this. I'm going to try to avoid spoilers, but potentially anything could spoil a joke so just go watch it before you continue reading. If you like over-the-top comedies, you'll love this.
Characters - Everyone in this show is just perfect. From the main character to the judges to the villains, everyone has a layer of depth that makes not only the comedy, but the drama work. While the characters in the show may find the clown judge's backstory annoying, it really serves to build up the character, provide comedy, and to be honest its interesting on its own. All the characters grow or develop in some way, and there are actually a lot more mature themes concerning death and family drama than I was expecting in a kids show. I don't want to spoil anything about the main villain, but she's evil and some of the stuff she does is incredibly twisted. I'm glad that it was handled so maturely by the writers.
Voice Acting - I have a lot of respect for the actors of this show. Out of context, they are all fantastic. Lines are delivered with the perfect emotion and tone for every scene. In context, I would never be able to read a script like this and say my lines with such a straight face. Its not just intensely screaming facts about bread, and explaining complex bread making techniques, but most of the jokes in Yakitate!! Japan come from absolutely ridiculous things happening and everyone taking it seriously. This show is incredibly over the top and full of fourth wall breaks and parodies of everything from Naruto to Japanese fairy tales to Dragon Ball to Gundum to Lord of the Rings. I can't count the number of times when a character whispers to another "Are we ok on copyright? Are you sure we wont' get cancelled?" Everything is delivered with such sincerity from the voice actors that it is just impressive.
Story - This series follows your typical shonen story structure. Its full of tournament arcs that get more and more intense as the show goes along. Its done very well and is extremely entertaining. I want to avoid spoilers so I'll just leave it at that.
Animation - The animation is Yakitate!! Japan's weakest link. This was clearly a quickly made production and it shows. The animation isn't bad, its just that there isn't much animation going on. Characters rarely move, and plenty of time-saving measures are taken. Whenever the animation needs to be expressive and ridiculous it is and its hilarious, so this is more of a nitpick, I just thought I'd point it out.