There is a couple of reviews available for Dead Island's first full-fledged DLC, Bloodbath Arena, which essentially offers a survival mode for the title, starting with this piece from Eurogamer, clearly unimpressed in tone and score, 5/10.
The game has also received a hefty title update which addresses some of the many technical flaws seen in the original game, and removes some of the more obvious exploits. It's still a shaggy beast though, with jittery animation and visual bugs a constant distraction.
If you have the free code then there's no reason not to give Bloodbath Arena a try, even if all it really adds is a place to quickly grind your way up a few levels. As a paid download, however, it's uninspired stuff. Every game is adding a Horde mode these days, and considered against the competition this is a particularly basic effort.
Bloodbath Arena seems more like a mode that should have been included with the game (and would have been easier to figure out how to play), rather than as a DLC, but it’s still enjoyable to an extent and for those who prefer survival modes such as Nazi Zombies, will feel right at home here, just don’t expect it to last as long.
Finally, Co-Optimus is offering some impressions, both in video and text form:
Overall, the Bloodbath Arena is a fun addition to Dead Island. If you're still playing the game, you'll definitely want to pick this up. If you haven't touched the game in a while, it might be worth revisiting. It all depends on how much you like zombie stomping. There are also new weapon mods hidden in each arena, which is a nice touch for collectors. The DLC includes 10 more Achievements worth 250 points, or 10 Trophies (7 bronze, 3 silver).