How do I get more Level 3 houses? I can only build one of each and that's not enough for one of the challenges.

Is your brickyard still operational? Do you have enough money and resources to build a new house?

My brickyard and the three other factories are fully operational and I have a pretty good cashflow... I've build all the Undesirables.
I have a feeling that there's something I need to build or upgrade, I just can't figure out what...

There's a limit on the number of houses of a certain design that can be built, depending on the players.

Each player gets one of each type (For level 4 as an example, Mock Tudor, Scottish Lodge, Townhouse) and then there's a pool of four more each can draw on before the limit is reached.

So, for example, if you're playing a 4 player game.

In terms of council Houses:
Red has built 0
Yellow has built 1
Blue has built 2
Green has built 3.

In this case, there is one available to build for Yellow Blue and Green, while Red still has it's "personal" council house and the last available one to build.

You might not be able to build the houses you need because enemies have already built a lot of them.
In that case, send your Mr. Fixits out to blow them up. >:]