Since quipping has already been confirmed, I'm pleased. As far as quipping in relation to the stakes of a situation goes, I dunno. I could see quipping in a big battle being handled properly. I think of it in the terms of the fight Spidey had with Kingpin where he pulls out the cue cards, but eventually starts making more serious statements during the ensuing fight.
Mind you, there's not much you could say as a serious criticism toward a giant lizard, but still. (Unless they go for the Lizard with a brain.)
Also, mostly for my own benefit, I composed a list of the quips I remembered from the Raimi trilogy. (Note: 'Quip' here defined as a 'snappy statement,' more so than a witty comeback.)
'That's a cute outfit. Did your husband make it for you?'
'Hey, kiddo. Let mom and dad talk for a little while, will ya?'
'You have a knack for getting into trouble!'
'It's you who's out, Gobby. Out of your mind.'
'Here's your change!'
'Oh, you know, work out. Eat your green vegetables.'
'I have a knack for that.' (in response to Ock)
'Look at little Goblin, Jr...you gonna cry?'
'You must not have heard. I'm the sheriff around these parts.'
