I have taken a running lesson with a pro and his comment was that I should be running inclined more forward. The way it is now (as I've found after the fact) is that I run pretty much perpendicular to the surface. Not that it bothers me, I have successfully finished two half-marathons, but still wonder if I should give my posture extra time in training or if this is something individual to every runner and some people just naturally run like I do. It definitely looks a bit strange on video, but doesn't seem to be a problem in practice. If possible, add some tips to help me self-correct my posture (preferably without someone taking video of my running, so that I can do a quick check everytime I run.)
Try stretching your soleus out a bit. The correct angle I've been taught is roughly 5-10% forward lean. It affects a lot, from heal strike to minimizing vertical bob. I'm not sure if you're bobbing around a lot but any energy sending you up and down is basically wasted.
The catch is you don't want to lean forward at the waist or back, you want to lean forward at the ankles. This can frequently be a problem for folks with weaker glutes and hamstrings.
I don't know if you do any types of strength training, but check out this study's findings:
Also, a significant positive correlation was found between hip extension and anterior pelvic tilt during both walking and running, indicating that anterior pelvic tilt was greater in subjects that displayed reduced utilized peak hip extension.
The best things I know for dealing with anterior pelvic tilt is strength training (or never sitting in chairs ever again). You want your glutes, abs, and hamstrings tight. Check out something like Starting Strength. I don't know if your running coach advised any training for helping your posture; there's far too wide of a chasm between running and the weight room.