That works if you have the supply available, but I think you would be happier in the long run if you got the signal to "noise" up by using a larger sense resistor. If you were to use the "good" TL272 and a .1 sense resistor with a gain of 10 you would probably see a 10X improvement and it would be there over temperature. Or, if you can afford the voltage drop you could use 1 ohm and eliminate all the offsets.
Anyway, you might want to add the load resistor to ground that Mike suggests even with the 272.
This current sense circuit is for my ATX power supply extension so I'm going to have regulated +- 9 volts available so that's not going to be a problem.
I was also thinking of switching between 2 sense resistors depending on the amount of current that i'm expecting. A 0.01R and 0.1R and control them using a switch.
Another thing is that I don't really need precision at the moment. I would be happy with a +- 10% error to be honest.