Your review is pretty accurate. It's a fan's sequel, and it does essentially everything one of those should do. The downside is that people who didn't enjoy the first one's premise of "lots of guns & fun with friends" probably won't enjoy this either, but there's a chance that they might appreciate the changes made. It takes everything that was good in the original and either refines it or replaces it with a superior system.

Gearbox really hit its stride with the series with its General Knoxx DLC from the first game. In that, your main antagonist would regularly communicate/heckle/chat with you over coms. The humor was consistent, the loot was flowing, and the game really started coming together. It seems that they took notes on that and expanded all of it to the sequel. It doesn't hurt that they hired Andrew Burch (of Hey Ash, Whatchya Playin') to pen the story this time around, so it's more interesting than the original. The humor may range from inane to zany to occasionally brilliant, but it's no longer the minor feature that it was in the first game. It's pretty much everywhere.

I really can't complain about anything except the inherent limitations of the level scaling. When your friends get too many levels above or below you, it's problematic. As it stands, though, it works really well for balanced teams. My advice for playing co-op with dedicated partners is to have alternate characters. That way, you can screw around on another character if your buddy has less time to play than you do. As a plus, as long as you have the time to do it, it helps you learn the other classes along with earning extra BA ranks.

One point you didn't address -- Badass Ranks. These are essentially replacing the Weapon Proficiency feature from the first game. In BL1, you would gradually gain extra accuracy, damage, crit chance, etc, by consistently using the same kinds of guns. (focusing on sniper rifles, smgs, pistols only, etc) In BL2, you instead earn account-wide bonuses by completing little in-game challenges. They're essentially achievements that earn you "Badass Rank," which in turn earns you BA tokens. When you redeem the tokens, you have five random attributes to buff slightly. (shield capacity/recharge, maximum hp, crit change/dmg, elemental effect chance/dmg, accuracy, gun damage, etc) By having a choice in these, you get to customize the small advantages that all of your characters receive. (usually in amounts no more than 1% at a time) Because these apply to every character you make, you no longer "lose" the effort you would have if it were the weapon proficiencies that were character-specific. While I'm sure the crazier challenges might require going out of your way to achieve, I've fulfilled many of these just by playing through the main story quests.

Also, they made ammunition more of an active mechanic this time around. In BL1, I don't recall having a lot of issues running out of ammo. Now, at least in my playthrough of 4 characters to their mid-teen levels, ammo is a much bigger deal. As a result, alongside the obvious act of upgrading your ammo capacity via the black market, you have to do a few things. 1) Make your shots count; 2) Class mods that add to your team bullet regeneration are more important; 3) Switching guns is more important this time around. Both 2 and 3 encourage having a Gunzerker in your party, as they tend to facilitate ammo regen. Also, because many powerful guns consume 2 or more ammo per shot, or come with modest magazines, the class mods and skills that increase your magazine capacity are more important, too.

As I said in a reply to iron, "friends don't let friends play Borderlands alone." The original game was probably a C+ when played solo, and an A in co-op with voice chat. (though YMMV, depending on friends) I would give Borderlands 2 a B+ solo and a solid A or A+ in co-op. That's not to say that it's perfect, but it hits its genre nail on the head so squarely that there's not much to criticize.