@deagol3: As the reigning King of Quickened spells, my character has a few answers to your questions.

First, yes, you'd have to assense the person, then assense each spell (all taking Simple Actions) to find out which spell to dispel in order to avoid trying to dispel the wrong spell.
Apparently our GM has House Ruled that having Quickened Spells raises the Background Count over time. My current residence seems to have a Background Count of 3, and most places my character is in for an hour or more gets a Background Count of 1. This is ok by me since I really don't cast too many spells. I started Quickening because the negatives I get by my Raven totem when inside, and we were always doing runs inside, so it was just better to cast before and try to stick to my guns while within. But still, kinda annoying that I have to leave home (and my Lodge) to cast a spell on me or someone, however, also kinda cool and I'm in no mood to learn Cleansing.

@Sunday Gamer: You are wrong about being a Beacon. This has been gone over time and time again, the rules about being a Beacon are a left over reminence of 2nd and earlier editions. In 3rd Edition you will find only 1 place that even remotely suggests that you are a Beacon, and that's the Astral Patrolling chart in MitS (pg 82), however you'll notice that there's not a "search time", indicating that as soon as you enter the area patrolled, on a successful roll, they are aware of you, wether they see you or not. You'll also notice on that same exact chart you will see that this patrol includes "complex terrain, building interiors", areas that you can't astrally perceive in without some time to travel. This indicates it's much more like a "hairs on the back of your neck" type of notice and not a visible beacon. All the other mentions throughout the books actually indicate a non-beacon theory, such as the rules for Astrally Assensing where you need at LEAST 3 successes to even know of something has a Force more or less than your own.
Easy to get Permits for the spells (after all, what sustained spell is damaging except Flame Aura which nobody would quicken). Astral Defenses is definitely a problem if you want to sneak past, but that type of character wouldn't go the Quicken route. Besides, once the defense is down, it still takes time to get the astral body there and back to locate where the breach happened (and even then, an opposed Stealth roll will keep you hidden from the Projectionist) and then to contact the people on-hand to warn them, hit the panic button, and then the defenders to get there. Etc, Etc. So yeah, it can be a pain, but doesn't have to be.
@Others: Anyone interested in Quickening rightly goes for Force 6 spells only for double the Karma cost to give it a Force of 12 to dispel. Now, in my history of Running, I've only maybe once come across someone with a Magic rating of 12+. Anyone else trying to dispel a "Force 12 for dispelling purposes" is going to take Physical drain, and I don't think people are going to be rushing to do that. Raise that Sorcery all you like, TN is still 12 to dispel, and you better have a Magic rating of 12+ to stay alive. It's only a sacrifice to Quicken spells like this if you do it at a Force any less than I've mentioned.
Sphynx