Here's how the scoring works in Spiderman.
Multipliers: You start with four of six white arrows solidly lit. Shoot them all to make the six white arrows pulse, which means the next one you hit gives you a 2x multiplier for that shot. Shooting all the lit white arrows also qualifies mode start at either orbit.
Starting all five modes is a requirement for the wizard mode, Super Hero. You don't have to beat the modes to get to Super Hero, but every time you do beat a mode it lights a 3x multiplier which you can again put on any shot by hitting it after the mode is finished. 2x and 3x multipliers only last until the ball is drained.
After the mode is over (timed out or beaten) the white arrows are lit again (5 of them for your second mode, all 6 for 3rd, 4th and 5th). You can't progress through the white arrows or start a mode during multiball, but you can start a mode and then stack multiball(s) on top of it to make it easier to complete. the Bonesaw mode is 'hit 100 switches in 40 seconds' and is made trivially easy if you can start a multiball right after you start the mode.
Multiballs: Doc Ock multiball starts after you hit the Dok Ock shot enough times. There are three versions of this multiball (first is two balls, second is three, third is all four) and they cycle; after the third one is over you can start the first one again with enough hits. The rules and strategy are different for each but they all have super jackpot collected at the Doc Ock shot, which makes it a good place to put a 2x or 3x multiplier.
Black suit multiball is started by hitting the daily bugle stand-up enough times and then locking a ball by hitting either orbit. The third lock starts multiball. You can stack black suit MB and Doc Ock MB in any order.
Battle Royale MB is the mini-wizard mode, started by getting through the first two villain modes for each villain. This one does not stack with other multiballs. There's also combo multiball at 50(!!!) combos, but I'm not sure whether you can stack it with normal MBs.
Spider Sense: Hitting all three stand-up targets on the right side will light spider-sense and add value to the shot. The scoring from spider sense is neat and unique, but the important part (to me) is that the shot gives you add-a-ball if you collect it during multiball. So if you start Doc Ock #1 and then Black suit MB, you get all four balls into play and can get one back (plus some ball-saver time) by hitting the lit spider sense. This only works once per multiball.
The spider sense shot is one of the trickiest and most rewarding shots to hit, especially during the chaos of multiball. Practicing this shot (which requires hitting the bottom of the raised upper-flipper, and then dropping the upper-flipper at the right time to send the ball through the lane) gives you a way to extend your MBs and get multiple and multiplied super jackpots.
Practicing this shot will also pay off if you make it to the end of Super Hero, as it's the last shot you need to hit to beat the wizard mode and earn that 250,000,000 and 2x playfield for the rest of your ball.