I get where you are coming from, Kramis. I read the requirements as "must weigh less than 20 lb and be able to be held in one hand (*interpretation* without it touching the ground) as of the moment when it is put into the glove". So the spiked chain would be ok, as would a greatsword or longspear (I'm assuming that those all weigh less than 20 lb. IDNHMBWM). A coil of rope would be fine, provided that it was coiled. A 20 lb pile of feathers would not work nor would 20 lbs worth of mice, but a 20 lb BAG of mice would (I'm like you: I just think it would be funny.). A shield would be fine with me too.
Your hypothetical length of rope would not work and I also wouldn't allow anything that was affixed to be put in the glove. So, for example, you couldn't go up to a locked door, place your hand on in and ZAP it goes into the glove.
Anyway, I guess I feel that I owe it to my players to be as consistent as possible. So I'd try and establish a rule (Under 20 lb, held in one hand without touching the ground, nothing affixed) and then go with it. If they figure out something that I never thought of, good for them. If it turns out to be horribly abusive then I'd talk with the players about it and try and fix it.
I think that your method of approving items on the fly is just as valid. But it seems like more work for me.