Hi,
I get moderate pain in my left shoulder for a few days after incline bench and dips. I noticed that when I lower my shoulders I can see a tendon(?) running from my neck down in front of the anterior delt. My theory is that when I do incline bench and dips these tendons are pushing hard into the muscle making it sore the next day. Could be from being too tight (i.e. need to somehow stretch them), or a less-than-great posture... I dunno, any ideas ppl? I'm sure this is not rotator cuff related...
Thanks!

Sounds like tendonitis.

Check out some of these articles.

how often are you doing dips and incline bench... or pushing movements involving the chest and triceps period for the whole week.

You need to really stretch the pec attachment, a chest stretch in a door way is good and done many times per day for 30 secs avg.  Also look at your scalenes for some massage, sounds like they may be a bit taut....I get that from coughing alot from asthma and allergies and its hard to stretch or relax those.
Also look into more water and minerals to help.
Linda