OK, well I think I know what your problem is: You're PWM'ing the motor, so you are reading the current either when it is on, off, or some transient in between. This will even out more as you get larger duty cycles (say >90%), which is why you're observing the current as being unstable.
My suggestion is to filter your signal. This will smooth it off significantly, but will add some extra lag into your system, so you will have to have a tradeoff between the filter speed and the filter ripple voltage. You can also improve this to some degree by increasing your PWM frequency.
You've already done most of the hard work. From your 1 ohm resistor you have an op amp which feeds into the ADC. Rather than feeding it in directly, make up an RC lowpass filter before feeding it into the ADC. If you choose a cutoff value of say 10 times less your PWM frequency, you should notice a MUCH smoother waveform. If you need help getting values, let me know what frequency your PWM is running at and I can work out some values for you.