Right now it's really easy to ignore because it's never really brought up that often that his webs are organic now. Like many people I prefer the good old web shooters but I do think there are some small things about the organics that could be explored...like since they're organic and not man made, does it mean they no longer dissolve after an hour? Are they weaker than web fluid? Stronger? Since he no longer has the adjustable nozzle, does that mean he can't make different types of webs anymore?
And probably the one thing I'd be most curious to find out, can he make webs indefinitely? If you remember, back when Spidey fought Venom for the first time, he was able to beat him because Venom used so much webbing trying to trap Spider-Man earlier that his "reserves" were running low, since the symbiote basically made the webbing out of itself. As Spidey put it, it was like a person losing lots of blood. Now I know Spider-Man isn't a symbiote, but his body has to be using something to generate those webs...something that has to be replenished perhaps? If so, then maybe if he uses his webs too much and/or too quickly he starts to get weak too, like the aforementioned person losing lots of blood? Or what effect would physical illness have on his ability to generate webbing?
I'm not saying devote a story arc to webbing or anything like that, but those types of things could be explored lightly here and there. I mean, if you're going to go with organic webs you might as well do something with it other than just "oh, I don't need web shooters anymore!"