I don't understand anyone who criticizes them for not having any storylines; if you've been paying attention to the shows and their YouTube series, they've been developing quite a few storyline strands to follow up on during the weekly television show. Other criticisms are kind of legitimate, but understandable as to why AEW is doing it, such as pushing Adam Page. He's probably be in the upper mid-card feuding with MJF properly if not for the Pac situation, but that seemingly forced them to switch around a lot of early storylines, resulting in Page being in the inaugural title match when he probably wasn't planned to be there at all.
As for my cons...
They really need to sort out their match style (overdoing the go-go-go kickout heavy style is going to burn out your audience quick; see WWE for reference) and sometimes how they structure matches as well. Not everything needs to be like Cody's matches, as seemingly Cornette and his little sycophant desires, but learning how to end on the highest note and why match types such as extended squashes and 7 minute formula TV matches exist would go a long way.
I'm not really sure what they're doing with the women's division yet, but as of right now the booking makes no real sense. I personally don't think Nyla Rose is at all ready, but push her strong if you're going to push her. Don't do this half-assed bullshyt they've been doing with her at DoN and Fyter Fest. Also, they just need better talent in general, as Britt Baker, Kylie Rae, Brandi, and Allie being the core of the division along with Nyla Rose just isn't going to cut it at all.
Building your tag division around a Best Friends/Super Smash Bros. feud is pure idiocy, particularly when you have the Bucks, SCU, Strong Hearts, Angelico/Jack Evans, Private Party, and the Lucha Bros. all right there just sort of having matches. The way it's been introduced, the way they've gone about the feud, selecting the SSB as the top heel tag team period, it all just seems woefully misconstrued. Maybe there will be more stuff when they get into the tag tournament, but it's not necessarily getting off to the best start outside of the ring (in the ring, they're prone to the match style issue as much as, if not more than, any other section of the roster).
Cody looks like he's totally going to do mid-late 1980s Dusty in WCW things with the book.
Giving himself premier matches in prime spots and hogging a bunch of show time with his mediocre "epics." At least Dusty was an all-time great wrestler and character. Cody hasn't really failed in this position yet (not even at All In), but I'm always wary when this type of thing happens.
The comedy is very hit-or-miss, and certainly not for everyone. I totally understand why they're relegating it to the pre-show (to not hinder the more serious stuff they're doing in the main cards), but this is where having outright dark matches can really help them out. Do the comedy for the fans, workshop it by, say, releasing portions of the dark matches that work on the crowd on line on YouTube or some other platform, then figure out how you might want to integrate it into the program (Fyter Fest, in a sense, was an entire show of this, at least when it came to its parodic aspect). As of right now, while I had no problem with the Nakazawa/Jebailey match (anyone taking that seriously is a true idiot) or the Fyre Festival deal, the Librarian stuff dies a death with anyone who's not an AEW diehard (partially because Peter Avalon and Leva Bates aren't good wrestlers at all). They don't even necessarily need to change their style of humor, but they really need to figure out how to work that better for wide audiences.
On the whole though, I'm generally very optimistic about the whole endeavor. The developing storylines have my attention, the talent roster is great without being bloated, they have a very good mix of established talent, veterans, and fresh faces, they have a generally different tone from blatant focus-grouped WWE fakery, I love the concept of post-show press conferences and the reintroduction of time-limit draws (though some education of the audience will be needed for the latter)...they have a lot going for them, and I've quite enjoyed what they've put out so far. Every company has problems, but that doesn't mean they will absolutely hinder enjoyment of the overall product.