Delta_G:
No, that's a completely different issue. The relay has a set of contacts that are going to energize a coil. You can't energize a coil and set off a relay with random noise. That's a very different thing from a CMOS gate in the input pin.Besides, you'll always have HIGH or LOW on the relay if you hook it to an output. There is no other options. Output pins are always either LOW or HIGH.
Sorry, I'm talking about multi-channel relays. The relay takes, say, a separate 12V power source that drives the coils and then waits for a certain voltage on IN1, IN2, IN3, IN4, etc to come from the connected Arduino digital pins.
Those IN-pins: are they only looking for inputs of ~0V or ~5V? If yes, then it seems to me that they're being pulled in a certain direction whenever there is an absence of input.