The biggest mistake we see in the barbell chest press is the pathway the bar takes, like whether it glides back & up creating an arc pathway (correct) or is straight up & down creating a vertical pathway (incorrect). Also, engagement of the shoulder blades is a key factor when bench pressing. 

Video #1 Correct Form:

• maintain a tight upper back by squeezing shoulder blades (retracting/pinching the shoulder blades back) which causes the back to be slightly arched (which is okay to do)
• feet pressing into the ground during the whole movement 
• movement of the barbell is a “back & up” arc/curved pathway
• the hand grip on the bar is wider than shoulders (wider grip = more stretch and engagement of the pec muscles) but not too wide
• the angle of the elbow is tucked to the side at a 75-degree angle

Video #2 Incorrect Form:

• no engagement the shoulder blade causing a flat back (can cause rotator cuff tissue irritation in front of the shoulder)
• movement of the barbell is a vertical bar path instead of an arc/curved pathway
• vertical movement bar (incorrect already) is paired with either starting too low or too high near the neck/collar bone (both incorrect)
• arm form shown at end of the clip is with the elbow “winged” out to the side instead of tucked at a 75-degree angle