So, the top and bottom halves of the spoiler on my '84 Firebird TA appear to be held together only by the stand-offs. How are the two halves supposed to be secured? Adhesive/glue, bolts, just the way it is? Haven't taken it off yet to explore further. Is there any problem with it being loose the way it is?

well i don't know yet how you would fix it but, it seems that the front mounts are broken. these spoilers always are breaking in one way or another.

The mounts are not broken, the top and bottom are separating at the back edge between the mounts.

so the spoiler itself is separating?

its a plastic of some kind, and they are glued together. Over time them warp, and thins happens.

If its not warped to the point where you can get it back together, a good plastic epoxy should work fine to put it all back together.