First, check the battery (I'm assuming you have, but that's always #1). The Seiko shutters use an electromagnet to arrest the leaves, if the batteries are low, the initial meter, mirror shutter trip circuits depress the voltage so the last operation (holding open the shutter) does not happen. But usually I find the AE display will go out before the shutter miss fires, and typical low battery (besides the display warnings) are occasional blank frames (not all).
A good check is to take the film back off, point the lens at a window, and look through the back when tripping the shutter to see if the shutter opens. If not, check with another lens. Look for oil on the shutter leaves, they may be stuck.
Mirror lock is really a "pre-release", flip the leaver down, the mirror releases. If you don't reset the leaver before you wind the body, the mirror will release again at the end of the wind. It should not affect the shutter release.
Multiple exposure decouples the wind mechanism to the film back. You cannot wind&release the shutter if there is no film in the back, unless the multiple exposure is enabled.