After switching to my own domain, some links still point to my old address. How do I fix them?

Use Regenerate URLs. Right after your new domain goes live, the Settings → Web Settings → Custom Domain page shows a Regenerate URLs section. Click it and WCart scans your canonical URLs, page and blog content and menu links for the old domain and shows how many it found. Click Approve & replace to swap them for the new domain. Do this straight after the change, while the section is shown.