Is it just that I'm bad at placing turrets or are they kind of useless? They almost never fire at enemies, and often they don't even start tracking before they're taken out. It just feels like they take for ever to notice an enemy and if they're fairly mobile they can just run past easily.

i had pretty good luck with them. Make sure you place them against a wall. 

Turrets are an annoyance at best.

Grenades own turrets. Everyone has grenades. Anyone with 2 brain cells will just disable them.

They should mostly serve as a simple warning system, since you see when they fire, take dammage or are destroyed.

It also depends on the level of the turret.  Lvl 1 turrets are horrible and useless.  Lvl 2 turrets can actually hold their own and take a grenade before going down.  Lvl 3 turrets are mean.

Place them against walls, you can get new, better ones as you level up

If you don't have a better place to put you landmine at the moment, think about putting it behind your turret - if anybody tries to take it out from the safe side or hack it, boom.

Combine fire with your turret - if you're defending an area it can help you outnumber an attacker even if no teammates are with you.

Tuck them away in corners to cover objectives or command posts - even if it limits their field of fire it is better than having them out in the open were everybody will see them and toss nades just for the points.

If you start getting turret points, get back over to that area and kill them, the turret will rarely do all the work on its own, but if supported it can be a great assistance.