Maybe some random events where characters would leave the house for a while and you wouldn't be able to use them.

Balance the distribution of collectibles. I like the money and all but constantly seeing coins gets a little annoying.

I really hate it when a child is carrying a collectible and drops it when some event happens that causes celebration or parents call them to dinner or brush their teeth.

Agree with others about more interaction between the characters. I don't like that you have to force them to watch tv together or 'tickle' or train or party. Heck, they could all even play a board game together instead of one person always playing by themself.

More weather then just rain. And speaking of weather, have it rain less often. Every couple hours gets a little tiresome.

Have the option of sending the kid off to college or letting him stay at home. Maybe the tradeoff could be, if you choose to let them stay at home, their starting salary will be lower or will have a harder time progressing in their career.

Goals that can only be attained AFTER you buy certain upgrades. (ie making a pizza but that can only happen with a level 3 kitchen).