Driving Inductive Load with MOSFET: N-Channel vs. P-Channel
The 'noise' you see on the sense output is caused by the the op amp's inputs exceeding their common mode range. But how can this happen when the op amp has rail-to-rail inputs? 

When the the FET is turned off, the inductor tries to maintain any current going through it. To do this it generates a voltage that goes above the power supply voltage. D1 limits this voltage rise to about 0.6V, while recirculating current through the inductor. During this time the op amp's inputs are driven to about +12.6V, 0.6V above V+ (which is very bad because they are rated for an absolute maximum of 0.3V beyond the supply rails).      

To solve this problem, relocate the sense resistor to the other end of the inductor. Now the inputs will stay just below 12V, and the op amp should work properly.