I like Adventurer's League but my only gripe is that it doesn't allow D&D Expeditions for private play (home/online), only in-stores and convention play.
This makes it harder to run online pick-up games on an evening (4-5 hours) like LFR or PFS and rely on bigger published adventures only that the DM has to run only part of, which IMO doesn't give the same satisfying experience than a self-contained 4-hours adventures give.
I hope Dungeon magazines will publish short adventures legal for AL private play if D&D Expeditions doesn't change its model.
You can play Expeditions as a pickup game as long as you're willing to play at a local store and they have table space. It's admittedly a bit more work than putting together a pickup game at home. But frankly the Expeditions program is designed to help support public play, i.e. primarily at brick-and-mortar stores.
If the local stores are full (such as on Friday nights with Magic players), we've found that they're frequently willing to support D&D play offsite at some other public place. We often have Expeditions at a Denny's or at a cafe, sanctioned by a local store that simply doesn't have room for us, and we collect up everyone's DCI numbers so the store can report the play in the Wizards event reporter.
It is my understanding that it's not appropriate for stores to be giving out the download password to folks to run home games.You can easily find pickup games online at alonlinetools[dot]net (can't post links yet) which is the main D&DAL online site. You can also find groups in The Moonsea Pub Facebook group, which is also a place where online D&DAL players hang out and organize games.
As for not allowing private play, that's not strictly true. It's up to your connection with your store - if they want to give you the season password, you can download and play games at home or where-ever you want to. AL also has a casual play or similarly-worded statement that allows your playing of published material (HotDQ, OotA, PotA, etc) to count toward AL, you just have to log it on your log sheets.
Hope this helps!