DRD Team

If you have something like a pointlight directly facing a monster, the pointlight will shut off completely until the monster is out of the way. I have no screen shot to prove this as all a screen shot could show would be a dark room.

EDIT: I have noticed that dynamic lights will function normally with a monster if the monster is dormant. If the monster is in any state including idle however, the bug occurs.

I am playing this weapon modification which replaces your weapons with Doom3 weapons. There is also a flashlight included, and when you
point the flashlight at a monster while it is alive, the flashlight's light disappears, but when it is not alive, the light is still there.
I summoned a Hell Knight...
While the flashlight is pointing at a different place, other than the Hell Knight, the light works: http://i45.tinypic.com/2zi92xs.jpg
While the flashlight is pointing at the Hell Knight, the light doesn't work: http://i46.tinypic.com/205boqp.jpg

I tested the flashlight on other things:
While the flashlight is pointing at a moving sprite, the light works: http://i45.tinypic.com/wa5xly.jpg
And you already know that when a flashlight is pointing at a dead monster, it still works: http://i48.tinypic.com/rli178.jpg

I knew about it long ago, I just wasn't registered to this website yet to report it.
There is a link to download this mod on this website: http://zdoom.org/wiki/Doom_3_Weapons_Mod

Here's my guess with the flashlight: It is created by an attack that makes an invisible bullet puff appear and the bullet puff has a dynamic light attached. However, I further guess that the weapon has not been set to "puff" on bleeding enemies so if you point it at a live monster, it doesn't work.

That's precisely what happens. Simple case of WAD bug.

How do you set the weapon to "puff" on bleeding enemies?

From the Wiki [zwiki]Actor_flags[/zwiki] page:

PUFFONACTORS
Used on puff objects only. A puff with this flag is spawned even if the actor being hit bleeds. Normally in such a case only blood is spawned but no puff.

You may also find flags such as BLOODLESSIMPACT and NOTRIGGER useful depending on how exactly you are setting things up.

Do you have to type it in the console? The page just says that you can set or clear a flag: +Flagname and -Flagname. What should you
precisely do to activate the flag in GZDoom? Should I replace "Flagname" with "Puffonactors"? Could you give me an example of what I
should do?

You need to give your light puff the '+puffonactors' and the '+bloodlessimpact' flags or you'll get odd behavior.