Judgment

Out of all the Like a Dragon [龍が如く] games, Judgement has by far the most coherent and well-written story. Yakuza 0 [龍が如く0 誓いの場所] and Yakuza 2 [龍が如く2] are the only other two I'd say have good stories.
The plot is very well-paced, to the point where the twists and explanations are either things I had guessed just a scene or two beforehand, or surprises that make perfect sense. The part I found most impressive was right at the end, when it's revealed exactly why the victims' eyes were carved out. It explained something that I didn't even think needed an explanation, in a way that makes total sense.

The thing the Yakuza games are most known and loved for is the complete tonal balance. The story is always serious and full of plot twists, but the side content that unlocks alongside the story is, in the majority, light-hearted and genuinely funny. The side cases and girlfriend stories in this game are no exception. Jokes only hit their full impact once, so I'll just move right along.

The main problem with this game is the Keihin Gang. Over the course of the story, Yagami will meet the four leaders of the gang, and beat them up. Unfortunately, this only angers them. At seemingly random points while you're exploring Kamurocho, you'll receive a text message telling you that the Keihin Gang is attacking the town.
This puts a "threat meter" on the screen, which starts at 100% and ticks down as time passes, or further down if you defeat Keihin thugs or bosses. The bosses are the same each time, and block off a road or alley, forcing a fight if you get too close. They just keep coming throughout the course of the game, with no way to get rid of them that I found at least.

The second problem is the game's new "mortal wounds" system. Since Yagami is only human, if he gets shot, stabbed, or hit with a powerful attack, he won't be able to heal fully until he either goes to the doctor or uses a medical kit.
The problem here is that the only doctor in the entire game is on the north end of the map, in the sewers. He's also the only person who sells medical kits. You have to run all the way to the north side of town, watch a scene to slide down the ladder, get treated for 20,000 yen, then watch a scene to get out of the sewers and continue on with your life. This adds up over the course of an entire playthrough, and gets very frustrating.
As a note, every Keihin Gang boss has an attack that will inflict mortal wounds.

The disguise system is a huge wasted opportunity, with so few instances where you're even able to equip a disguise.
The tailing mechanic isn't horrible, but some of the actual tailing missions are. I understand it with the final tailing mission, but too many of them are trial and error, with how much they turn around while there's no cover nearby. The one in the arsonist side case was especially infuriating.
Thumb-turn lock bypasses are godawful, but I only had to do around three. The regular tumbler lockpicking minigame is surprisingly pretty good.

One big side mission type is friend events. For most of these, you simply have to patronise a business, then keep dropping in periodically. Some, like Yosuke's, require you to make other friends or complete side cases first.
Some, however, are simply annoying. One requires you to find all 50 drone part QR codes scattered around town. One requires you to get five paintings, most of which require you to do the repetitive gambling minigames until you get enough chips. Another requires you to actually learn how to play Mahjong, which is simply not happening.
Worse, side cases require you to have a certain amount of friends. I'm sitting at 48/50 side cases, with 45/50 friends because I value my time more than the game seems to. They added "more content", but it's just padding in this case.