I don't seem to be able to press the weight, no matter how light, with correct form. I can't lock my arms out whilst keeping my arms in line with my shoulders. I'm guessing this is because of not being flexible enough but I don't know what to stretch. Can anyone suggest a remedy or replacement exercise?
A great way to increase shoulder flexibility is by grabbing a broomstick or if need be a rolled up towel, and start with your arms as wide as you need to. One rep is coming from your chest, up over your head and as far back as you can go. Let your hands slide out in order to get over and behind your head. A good target is 50 reps. Once you get close to this, start moving your hands in closer.
This should dramatically increase your shoulder flexibility.
BTW, I do not think that you should be fully locking out your arms during each rep, as it it optimal to keep tension on your shoulder muscles throughout the set.
Try the above and see if it helps your flexibility issue.
Depends who you ask. Keeping tension may be better for muscle gains, but locking out can incorporate and build tendon strength. So, locking out on most exercises isn't the end of the world.
I agree that it's likely a flexibility issue, presuming your starting with helathy (never been injured) shoulders. The move that Tharren recommended is a good start. Also, if you can find a copy of Tsatsouline's Joint Mobility book, it has some good range of motion drills in it.
Here's an articel by Ian King with some awesome pictures: http://www.t-nation.com/readTopic.do?id=459832
Can you straighten your arms overhead with NO weights? It could be tight biceps/forearms as well. Also, do you notice limited flexibility on any other exercises?