This will be specifically DC since I'm not currently reading much of Marvel outside of the Star Wars trades but that doesn't mean the company doesn't share a few of these problems. I try not to dwell on the relaunch issues but there are things still concern me.
There really isn't a sense of history which creates problems with the threat scope of the villains and the relationships between the characters. One of the biggest complaints I've heard is that the JL don't feel like friends, maybe they would if we had stories to see them evolve from point a to point b. Sure there's some effort being done with flashbacks and recent mini/max series but that only addresses a small portion of the problem and in some cases needs more retcons to work. A big reason is because no one seems sure how anything works in the timeline. No wonder we haven't seen much of the Time Masters, how can they explore time if the writers aren't firmly committed to one ? This one likely won't be solved for awhile once more stories are written to fill in the gaps.
This was a huge appeal to me when I was first starting to read DC. The only one we really have is the Robin legacy. The legacy doesn't need to be someone using an old mantle or being related. It's an ideal, an inspiration to strive for that's set down from one character to the next. Something to tie characters together and become something bigger. Without it there seems to be something seriously lacking.
This kind of connects to another thing on my list. I'm putting it separately because it seems to have become a trend. Barbara Gordon isn't near her Oracle level. Starfire went from commanding her own space crew in RHATO to someone who tries to drink baking soda because it has the word soda in it in her solo. Simply put I'm not a fan of this trope.
Lack of Character Consistency
In one title the character puts on a tough front but slowly opens up to people they grow close to. There's real depth and an insecurity with revealing their true feelings. If others are hostile they respond the same or act as maturely as their able to until they leave. Other books toss this all away to make the character act like a jerk, idiot, punching bag, etc. Canon from book to book might be iffy but you should at least have consistent characterzation. Too often I've seen clichés being used instead of doing research to find out that yes this character has depth. This pisses me off more than the lack of history and legacy. Because if the writing of the characters isn't up to par what else matters?
Yes I know, DC wants to promote a looser canon. In some cases like the lack of consistency with the characters it's good to know we can ignore the bad characterization. But that becomes a problem when the writers don't acknowledge connections between characters or important character beats. Did you know Jason was an unplanned pregnancy ? He wouldn't be callously referring to someone being "knocked up" especially in front of the child of that pregnancy. Roy is a recovering alcoholic so no, he wouldn't be causally drinking. Nor would his friend Jason (who despite being legally dead is also underage) try to get someone younger than him to drink.