What is my biggest beef with 5th Edition shooting? TLoS. Our local meta is not equipped to deal with TLoS. The lack of total line of sight blocking large terrain and the lack of education regarding 25% of the board covered with terrain makes it really tough for monstrous creatures.
I think a lot of the folks in the area want 40k to just be a shooting game. I want to shoot you out of my metal boxes with wheels and my dead dudes in coffins, and whoever shoots the most the best the fastest should win. Unfortunately that isn't really the way the 40k universe is. Entire armies are based on close combat and getting there. Tyranids can do a mid-range shooting army somewhat well but their true strength lies in close combat.
I've seen it posited that the 4+ universal cover save is too generous and needs to go. The only way this could happen is if other things happen - modifiers to hit, target priority, abstracted terrain, etc. In my opinion, TLoS just really needs to go. Warmachine does abstracted terrain really well. Flames of War does it well too. I get the idea of getting down and seeing what your guys can actually see but it doesn't represent your warriors ducking, moving around, hiding behind walls and the such. It just doesn't work.
I don't have a ton of suggestions right now as to how to fix that, but abstracted terrain is the first. Woods should be able to hide a carnifex. Make terrain actually matter - force choke points and the like so that we can actually feel like generals as opposed to alpha-strikers.
Related to the shooting phase would be psychic powers. There are so many psychic powers right now that your head could spin. For Tyranids alone I have to remember to use one at every certain point or they're wasted. Some are psychic shooting attacks when they should just be done in the movement phase. Solution? Make a psychic phase where all psychic powers happen. If you think you're going to assault, cast hammerhand. Right now the whole psychic power mechanic just feels tacked on and terrible.
Modifiers to hit would make the game so much more tactical in my opinion. If you moved this turn, it is harder for you to shoot. If the enemy is behind soft cover, they're harder to hit. If they're behind hard cover, they're even harder to hit. The cover save or armor save mechanic doesn't really hold up.
I don't generally wax poetic on game balance so these are my ramblings right now. I'll focus on Tyranids and Space Marines in 6th Edition in another post.