1) To give someone the hard eye is to look at them with disapproval/disdain/dislike. You give someone the hard eye when you don't know them- you just know you don't like them. Like when someone won't stop swearing when you've got small children with you. That merits a serving of hard eye.
2) To appraise something critically. One assumes that aspiring models are given the hard eye when they apply to an agency. It's when you look for things to dislike rather than things to like.
1) The mouthy teens on the bus continued to talk at deafening volume and play offensive rap music on their mobile phones, despite being given the hard eye by 90% of the passengers.
2) After giving Vanessa the hard eye as she walked to the loo, Doug decided he wouldn't be taking "her" home after all.