Hey Tim –
When people like your page it will still show up in their feed, and it will show up in the mini-feed. However, you are right about your second point. Unfortunately page content will not be showing up in every persons feed even if they like the page. It is based on something called EdgeRank, and it uses a half-secret/half known method on who will see what you post. You can learn more about Edgerank on this site.
There are two main reasons why this is occurring. Facebook wants to make more money from using their ad platform, and second it is Facebook’s attempt to clean up and de-clutter feeds. Unless someone has previously engaged with your content in the past, or you post about things they have interacted with you have a much lower chance of it being viewed.