Trying not to echo what other have already said, there's quite a few issues. I played it for a good 3 hours last night, it finally clicked a bit and I won 4 in a row.
There really needs to be more actions you can do in this game. I understand they want the simplified "pick up and play" aspect, but in the car all you can do is boost forward, and boost to the side. Once you use both of these, all you can do is simply drive while you wait for cooldowns, so it's pretty boring during this moment. Sure, someone can hop onto your car and you gotta fight to stay in, but the controls for that are not clearly explained. I don't know what I'm doing when it flashes square or circle. Mashing the left stick to shake off is self explanatory though. You can also jump out of the car temporarily to collect gems to build meter, but I don't really want to do that if I can instead spend more time hitting people and building up my score.
On foot can be kinda fun, but I find that the melee attack and special move isn't very useful because you're almost never near someone else on foot. It feels good to wall run and jump, but a lot of gems and platforms are *barely* out of reach which is very frustrating. I get that those areas are reserved for people who went the "correct" route and platformed their way to those areas, but it's sometimes hard to tell where you can reach from the ground.
Minor nitpick, but make the damage counters increments of at least 10. Getting 1 point for a light hit feels very underwhelming. If it said 10, I'd feel better about it.
Stage hazards aren't very fun or interesting. Big hole in the ground, huge spinning blade, cylinders that pop out of the ground, they all just feel like they're in the way. I want boost pads, or ramps, or something like that. Though it may make it more difficult to hit people if there are movement enhancing hazards, so I get it if they didn't want to put those in.
There's so much focus on the characters and not the vehicles. Sure, the vehicles are expendable in this game and you only get your hero car once in awhile, but it would be nice to at least see a model of the hero car at the character select screen. The background video of the hero car isn't as crystal clear as just a slow, rotating model of it like other car combat games. I had to go to the practice mode character select to see what all the abilities are, since there's not enough time during an online match to read every character/car's abilities. Then I had to go to customize mode to actually see the hero car models. It would help if there was just a "Characters" mode where you can just look at them and their vehicles to see what they do. Or just put their abilities in the customize mode.
I know this game started as a Destruction Derby project somewhat, and as someone who enjoyed these types of games back in the day, it's a mixed feeling. They do have some cool ideas in here, but it just needs more polish and gameplay elements. I'm a huge Twisted Metal fan, and it would be cool if they looked at that game a bit for inspiration as well. There's very few dull moments in Twisted Metal. You're always trying to do something, be it looking for items, boosting, shooting, chasing down, ramming, healing, deciding what weapon to use, etc. I'm not expecting all of this in Destruction All Stars, but the idea of always having something to do would help.