Back to the point of the original OP, he needs to learn about the fundamentals of op amps. As the contributors above have said, the main reason for your error is input offset voltage. This is a *DC error* that is effectively added (or subtracted - and it can be either) from your input voltage. So with a 1mV input and a 5mV input offset voltage, your amplifier could effectively be amplifying a 6mV or -4mV signal. Input bias currents, with the resistor values you are using should not be an issue (it amounts to the input bias current (100nA) x the parallel combination of the 837k and the 2.14k.) This only amounts to a 100uV or so.
Also, how are you generating the 1mV? If it is from a high value resistive divider network, are you measuring the 1mV with a fairly low input impedance voltmeter? this could also be contributing to the errors you are seeing. If you apply a low impedance voltmeter to the junction of 2 resistors, the junction voltage will change as the meter loads the resistor divider.
Generally LM324s are not good for amplifying mV dc voltages because of the input offset voltage.
Dont worry - this is teaching you much more about op amps than you can read in a book and professional engineers still get this stuff wrong!
If you want to amplify mV, I would use an op amp with a lower input offset voltage.
if you want to learn about the LM324 (and it is one of the world's most popular op amps), use a higher input voltage (1V or so).