Cast/runan eye/your eyes over something
Definition 1 of 1
Pro Tip 1/3Brief Check
Use when suggesting a quick review without going into detail. 
Could you cast your eyes over this email to ensure I've covered everything?
Pro Tip 2/3Casual Tone
The phrase adds a casual tone and suggests the task is not burdensome. 
When you have time, run your eye over these photos and tell me what you think.
Pro Tip 3/3Non-Comprehensive
It implies a surface-level engagement, not an in-depth analysis. 
I'll cast an eye over the proposal during lunch and get back to you with any thoughts.