That's why all the good airlines (
)have a flight ops/dispatch officer who is responsible for assigning a priority to NOTAMs which affects the way they're printed. (1s get a grey background, 2s are normal, 3s are not shown at all) And also have said officer go through and run a highlighter over the major things. They still get the full list to read through when they're bored, but all major stuff is easy to see. If you just get a non-descript dump of NOTAMs -- no wonder your eyes glaze over!
That's not to say things won't be screwed up at some stage, but I do like the system we use at my airline as it cuts down on the info crews have to absorb at briefing. Stuff like AYPM FIR navaids almost all U/S...I don't bother with since they're always like that and we're just flying through anyway. A shortened RWY or closed TWY -- Green highlighter at the ready!