Don't want to butt in too much, but wbeal1:
Probably a better powe supply as mentioned, and the caps.
But just a small thing about your schematic.
I understand what you are doing - or I think I do - but how you have drawn the "relays" and motor are confusing.
The motor is 120 vac. Well the circuit is 5 vdc and you haven't shown from where the 120vac is coming and how the motor is really connected.
There is no + and - with AC, so the + and - signs on the motor are confusing.
On "relays" you have 4 wires - which you show - but 2 go to the "coil" and 2 are the contacts, switching the high voltage.
So, what I see your circuit doing is:
There are two valves, Upstream and Downstream.
There is a control for the motor to pressurise the pipe.
There are two ways to depressureise the pipe. A toggle from the pressurise switch and a "test" one.
There is also an emergency stop button - good idea.
The pressurise swtich can be active but at the same time the "depressurise for testing" switch can be active.
Is this supposed to happen?
And the motor, relay part mentioned above.
Suggestion - and it is only that.
As neat as you have been with keeping the pins in sequential order on both the Arduino and LCD, it would make it a whole lot neater/easier if you bunched the "wires" together rather than honoured the pins.
D10,11,12 would go from the Arduino straight out, turn left and go straight to the LCD, BEFORE pins 1,2,3 on the display's chip. Well that's optional.
D5,4,3,2 from the Arduino would also be tidied up and go from the Arduino to the LCD. On the horizontal part where they continue on to the relay, drop the line to the inverters/LED's.
When you get to the relays, space them out a bit more and then put the valves beside the respective relay, and not "up there in another part of the circuit".
Then there is the problem with the AC voltage. I am sure there is a problem with how you have drawn that part.
I am only suggesting this because it will help with clarity of people's understanding of the circuit should they need to look at it.