"Take one solved mystery, and shuffle it back into the mystery deck"
Honestly, my group just ignores the reference guide clause where it says mystery cards shuffled back in or removed from game no longer count as solved. Having to redo the same mystery is punishment enough, IMO, let alone having it count against your solved mysteries. Also, since Azazoth has no Final Mystery, it's almost a guaranteed loss when playing against it.
If anyone has actually won the game after shuffling in a solved mystery, I'd really like to hear about it!
As for the second thing, I'm tempted to just throw in appropriate research/clue cards from other Old Ones for variety's sake until an expansion comes out.