Issue of power line noise
A few mVolts for an MCU is nothing. Even 100mV is nothing in such a circuit, unless you want to use it to measure small signals precisely. However, I cannot see the mandatory 100nF ceramic capacitor as close to the Vdd-GND pins of your MCU, as possible. That capacitor makes a difference!

If you are concerned about the noise related to the LCD backlight, then avoid PWM brightness control of the backlight. Use a series resistor or a pot to set a fixed brightness.