The anterior deltoids are used extensively in exercises like chest press. Two problems can arise here, firstly trying to train shoulders after chest will result in a considerable drop in strength compared to training them first, so you can't get weight up in the military press for example to be able to then work the lateral deltoids.
I reccommend two things, firstly training shoulders separate to chest and
try doing 'isolation' work for the lateral deltoids like side laterals. You can do these with regular pressing movemet. If you bench press is strong and your overhead press is weak its probably not the anterior delts but the lateral delts so you may want to concentrate on these.
You can also do bent over laterals for the posterior delts.
Another point, If your anterior deltoid is weakened from overtraining in the bench press, then doing overhead presses become difficult and a bit pointless.
Injury wise,problems can occur if there is an acromioclavicular joint sprain since the anterior deltoid muscle cannot contract properly in an unstable joint.
I aldo recc using only free weights to train the shoulders. Free weights are beneficial to the the small synergistic rotator cuff muscles that also need strengthening as well as the delts.
These small muscles don't get much use in machines because they are mainly in a stabilising role.
There are also specific exercises to develop the rotator cuff muscles which you can usually find articles on, here or on the net.