If you click on "Download / export this family..." at the bottom of the left sidebar, you can export your data. The first choice, "Read-only HTML page" will give you a file that you can open in a browser to view. The other formats on that page are mostly for use in other programs.
This still has the limitation that you can not see everyone in a very large tree at the same time. But I think that is a fairly standard limitation. For instance, in Family Tree Maker, you can view less of your tree at once, however, they do have some nice charts that you can print.
