I'm bored so I'll share.
I have found a few simple things make keeping the LCD like new are key. First: wear gloves. I know this sounds basic but a lot of people skip over this. Cleaning a few specks of dust is easy as pie compared to getting finger prints off. Second: Use air whenever possible. Do not use canned air, use either the squeeze one linked above or if you are going to do this a lot, invest in an electric one. I use mine all the time to blow out glass, dust and whatever else lands on the LCD. Once I have gotten everything off I possibly can with air, I coat the LCD in Zeiss lense cleaner. I make the whole LCD wet. I then used a micro fiber cloth to soak up the cleaner and get anything else on the LCD. Micro fiber will leave some streaks, so I finish up with a fine lens cloth. I can take an LCD from totally nasty and gooped up to looking like new in under 30 seconds. If you do get a smudge that is being stubborn, 100% acetone is your friend. It works like a champ and doesn't streak.
I clean the LCD as the last step before I seal the iPad up. That way dust doesn't have time to land on it. Clean the LCD, rip off the film from the back of the digitizer, stick in place.
As far as getting the adhesive off, that's even simpler. Scrape everything you can off with an "iPad opening tool". I don't know what the real name of it is but if you search for those, you will find them. I've never used one to open an iPad but they are awesome for getting adhesive off. Once you have all the glass and adhesive you can get by hand, dip a Q tip in Goo Gone Pro Power. Run the Qtip over the whole ridge, apply heavily where you see big splotches of adhesive. Let it sit for a minute or two (I use this time to grab the digitizer, grab coffee, watch a funny cat video), then go over the whole thing with the opening tool again. This will get any an all adhesive off with zero chance of tearing cables or ripping antennae. Immediately after that I take a cheap shop towel and dip the edge in 99% IPA. I go around the ridge with that and scrub anywhere there is still goop. I go around once more to make sure all the Goo Gone is gone so the tape will stick. Most times its a total of 2 or 3 minutes and the ridge is perfectly clean.
I keep saying I'm going to build a desktop clean station. Maybe I'll do that this week???......