It sounds like you're clicking somewhere or on something else or somehow not actually selecting something. It's hard to say. To draw a landmark, the steps are:

1. Hover over the + button from the toolbar
2. Click on "Landmark" in the menu which appears
3. Click on the map where you want to draw the landmark
4. Move the mouse and click to drop another geometry node to define the shape of the landmark
5. Repeat 4 until the landmark is complete
6. Shift+click to end drawing the landmark
7. Click on the landmark to select it
8. In the General tab, select the proper landmark type
9. Click in the Name field and enter a name
10. Click into the Description field and enter additional information/address details, etc.
11. Hit Tab on the keyboard or click on a non-object area of the map
12. Click on the Save button

Thanks for the help, Dan.
I've tried what you described above, but unfortunately it still doesn't work. I've tried to do this in multiple browers to make sure that's not causing the issue. Any other idea what could be problem here?
By the way, I had the same issue with changing one-way streets into two-way streets. The only way I could eventually solve that was by using the toggling keyboard shortcuts.

After you type something in the field, make sure you click outside of that box before you save it. For example, draw the landmark, give it a type, name it, address it, give it a phone, then just click in the description box without typing anything. The fields are set to update on exit, and clicking outside of the field is the exit. Clicking the save button is not an exit allowed for the field update, so your changes will be discarded.