Currently the only bug I've been made aware of, is if you do Violet's second quest, where you visit/help her with the bookcase, before you do the "Sigh..... go to sleep quest", the game will soft lock. I've fixed this issue in v0.03, which I'm currently working on right now.
As for you not being able to get to the market, do you mean you cannot complete the "Visit the merchant named Bront" quest?
Have you clicked on the wooden shop with a blue/white striped sail next to the outdoor market named "Bront's shop", which you need to click on and that will enable the quest - (The actual outdoor markets aren't available until you visit Bront's shop).
However, if you do visit Lily and learn about her debt, you then have to visit James, as everything will be temporarily locked until you visit him and complete the quest.
As for registering at the Guild quest, this is the last quest for v0.01 and everything else has to be completed beforehand, so it won't be available until these other quests are done.