Shunt measurement with cheap op amp
0.25A * 0.001 ohm is 250uV, which isn't too bad. 

Vos of the E version is 75uV maximum, and you can null that out. The more difficult one is TCVos which is maximum 1.3uV/°C. If you allow 20°C change that's 26uV, which is 26mA on your shunt. 

The OP07 is a very old op-amp but not a bad precision op-amp especially if you have the dual supplies available. To get much better you have to use a chopper type of amplifier, which can have other issues.  

You should be fine. Make sure to follow the data sheet requirements on supplies (especially common mode range) and (very important) make sure you use a proper Kelvin connection to the shunt. 

Edit: Here is what I mean by Kelvin connection- this amplifier has a gain of 50, so 5.0V out for 100A through the shunt. R2-R5 represent connection and leadwire resistances, not real resistors. 







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