Hi again,
Yes the resolution on those devices isnt that good really. Have a look on their website. Those sensors are really made for currents a bit higher than 70ma, like maybe twice that minimum.
If you are going to use a uC to measure the current and you want to use a resistor in series with the power device (such as soldering iron) then you have to think about safety also. With the resistor connected to the line and the uC connected to the resistor, that means the whole uC circuit is live and certain extra precautions have to be thought about such as using a plastic case and other things. Im not sure if you want to do it this way or not. There are also current transformers that can measure the current and also isolate the line from your uC circuit. With a current transformer you have the option to wind more than 1 primary turn around the core which gives you better resolution which means the ability to measure low level currents like 50ma.
If you do want to use a resistor like a 1 ohm 5 watt resistor, then to measure 50ma you have to also use an op amp to boost that 50mv up to some reasonable level that the uC ADC can measure. For example, if you boost it by 10 the ADC will see 0.5v, and if you boost it by 50 the ADC will see 2.5 volts.
If you boost it by 10 you will get a range from 0 to 0.5 amps, but if you boost it by 50 you'll have to include a way to switch ranges so you can measure higher currents too. This means making the uC switch the amplifier from a 10x to a 50x, or from 10x to 100x, or whatever works best for you.
If you boost by 5x constantly, then for 50ma the ADC will see 250mv, and for 500ma the ADC will see 2.5v, and for 1 amp the ADC will see 5.0v. That means the ADC will have less accuracy at 50ma and more at 1 amp, but sometimes it doesnt have to be super accurate anyway.