There's a chance a villager will leave. Only one though, and that's only if they decided to leave before you stopped playing (whether or not they told you).
If you don't have beautiful ordinance set, your flowers will wither and weeds will grow (they'll grow anyways, just at a much slower rate)
You'll have bed hair when you play again.
Pretty much it. Make sure that if you do set beautiful ordinance, you still water your stuff the day before because that dryness carries over to the next day. And launch it once on the day that the ordinance goes into effect, otherwise it won't until you begin to play again.