Laser Woes

Have you tried connecting the arduino ground to mains ground?

What do you mean by that? Also this is the schematic I tried for the flyback diode. I used a 333 ohm resistor.

Forget the flyback diode it is probable in that expensive switching unit. It will not cure anything for you.

What do you mean by that?

Well you take a wire from the mains ground pin and you connected it to the Arduino ground pin.
Can't be clearer than that can I?

Sorry, I'm still learning all of this language. I understand what connecting the grounds means, but I'm having trouble understanding what connecting the ground pin of the arduino to the "mains" means. Do you mean connect the ground returning from the relay to the ground at the wall socket?

That's about what he was talking about, yes.
He means not the ground which is switched by the Arduino (which therefore isn't a real ground), but that of the system.
That means all grounds from Arduino, shields and so on will be connected to the protection ground of the wall socket.

Timesweeper:
Also this is the schematic I tried for the flyback diode. I used a 333 ohm resistor.

Just to make sure.
The flyback diode is D1.
The diode D which is coupled with that 330 Ohms resistor, will light when the relay is supposed to turn on.
That one doesn't do anything to prevent EMF issues.
So resistor 'R' and LED 'D' can be left out, but won't do much harm either.

On the Arduino there is a pin labeled ground. Take a wire and connect that to the ground pin on the mains socket.

Tried it, no luck. Thank you for the suggestion though.

jremington:
If it is a household AC motor and switch, then interference could be radiated by the motor leads, AC switch wiring or could be coming through the AC line itself. In the latter case, an AC line filter for the Arduino power supply may help.

Is the AC line filter built into this UPS sufficient? http://www.apc.com/resource/include/techspec_index.cfm?base_sku=BE650G

I noted a lot of background noise when I tried grounding everything directly to a wall outlet without the filter.

Timesweeper:
Tried it, no luck. Thank you for the suggestion though.

Keep it in.
Tacking issues like this is seldom a single fix, it is cumulative.
The next step is to add extra supply decoupling to the arduino's power supply.

Sorry for the delay! Do you have any good resource guides/how-to's on setting up supply decoupling?

Start here
http://www.thebox.myzen.co.uk/Tutorial/De-coupling.html

Does this seem like a good start? The lower resistor corresponds to the laser trigger.

Can you explain why you think this is the way to go ?
What is the function of each capacitor and that inductance (the coil) ?
Is that other resistor a resistor or some other part you wan to control ?

You telling about that might help to get some answers to your questions.

Sorry, I am just integrating all of the suggestions (flyback diode, common ground) with Grumpy Mike's suggestion regarding decoupling.

The solenoid corresponds to the XAC1 relay which drives the AC motor.

The resistor connected to digitalout 13 corresponds to the laser, it takes 5V pulses and translates that to firing the laser.

The unit on the top left is the proximity sensor.