Indeed looks like a few problems there. Your push buttons likely won't work like that. Each push button needs to connect to its own pin on the Uno so the software can tell which of the three is pressed. Basically one end of the push button goes to ground and the other contact connects to both an input pin on the UNO and a pull up resister to +5V. As well you need more connections to the A4988. If you only want full steps on the motor you could ground the EN, MS1, MS2, and MS3 pins if you want microsteps you would need to connect Uno digital output pins to MS1, MS2, and MS3. You need a pull up resistor to 5V (or a UNO output pin) on RST and SLP (a 1K resistor to +5V is probably best, I doubt you care about sleep mode). The LCD needs the wiper of the pot to go to pin 3 (not the backlight where it currently appears to go) and you need Uno pins connected to pin 4 (data/instruction select) and pin 6 (Enable) . The backlight looks to be connected directly between 5V and ground which will burn it out. The 330 ohm resistor needs to be between the lcd and +5V to limit the backlight current. If you have software for the Uno, then you need to assign the I/O pins on the Uno to the hardware on the pins which the software expects them or change the software to match your pin choices. Good luck!
Peter Van Epp