Scampy, these solid state switch come already equipped with a current limiting resistor already integrated inside the switch.
If you place a led with its resistor in parrallel to the ssr there is the possibility that the current circulating in the ssr branch is not enough to trigger the switch. (Mind these switches work from 5 Vdc to 32 Vdc) since you are using 5 volts (from the arduino output pin), you are in the low current region, so anything that drop a little more the current to the ssr will have the effect to un-trigger your switch.
Follow the amgen advice, connect the arduino pin to your led (+terminal) and the led (-teminal) to the ssr (+terminal) while ssr (-teminal) to ground.
Alberto
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