Most Gls and Rocket launchers have a safety trigger that activates the warhead only after the projectile has traveled a set distance: it MAY be that this feature is damage implemented, but the visual explosion triggers anyways because it wasn't correctly deactivated (yet)...

This ticket is only relevant to recruit setting. NOT ELITE OR VETERAN

Throwing grenades at enemies also has absolutely no effect if it's right next to them.

Could it be that explosion damage has a maximum AND minimum radius, and for some reason the latter is set too high then?

I can confirm this, on elite also.
A hostile missile went off 2 meters from me and it didn't damage me at all.

I was able to repeat this yesterday in a mission I made. Normal difficulty, AI squaddie was prone next to me. I dropped a frag right on his back and ran. BOOM, he's still there. Dropped another directly on him, BOOM! I hear "wounded!". Dropped a third frag on his back and he finally dies.

Apparently the safest thing to do when a grenade is tossed at you is to dive on it.

Confirming this issue. It has been reported as a bug.

Confirmed status -> acknowledged :)

Explosions are terrible, this also includes the grenade launchers. I dropped a grenade by my feet laid on top of it and it did not kill me.

I've witnessed this first hand as well. I landed two 40mm grenades right on a 4 man patrol, which should have killed at least 3 of them if not all. But none of them died.

This issue is fixed.

Mass close.