Some of the problems I struggled with in the very beginning:
- series numbering (how to switch from Roman to Arabic numerals - easy as such but it wasn't easy to find this option),
- lots and lots of tags which didn't even make sense (solution: customizing metadata download),
- tag browser view: switching to sorting by popularity / average rating without realizing it (but it has changed in the last Calibre release and probably will be less of a problem),
- collapsing/partitioning of tag browser categories (especially in my beautiful genre custom column with hierarchical items

) - again, very easy to switch off but one has to know where to do that (and what's happening)
- adding additional files/formats (just drag&drop but you have to know where to drop

)
Plus, just like Kiwidude I turned one mess into another, trying to import all books to Calibre ASAP and clear up data later - not a good method, especially for beginning users of Calibre - the mess in the beginning is so overhelming you may give up before you actually start enjoying it.
Some discoveries I was very glad about (they weren't problems as such but improved my work with Calibre immensely):
- how to easily show/hide columns in the view,
- how to bulk modify a tag without using the search&replace option (by simple renaming it in the Tag Browser),
- custom columns!!! + column colouring + plugins
When I discovered that (fortunately, pretty quickly) I was in my own OCD, "let's play with all these columns and create the perfect book catalog system I've never had" paradise.
My discovery of this week (still don't know what to do about it

):
- there is a quickview option!
The biggest problem of beginning users of Calibre of all times is probably:
- how to change folder structure in Calibre (the answer is: you can't and you shouldn't try),
Plugins that I find particularly useful (but this is a very individual thing, depending on one's needs, and this keeps changing in my case):
- Extract ISBN
- Reading List
I use many others, too (Generate cover, Open with, Count pages, Modify Epub, Quality Check) but these two are absolutely indispensable.
Other than that, I agree with theducks: as a beginning user of Calibre (but even now!) I would love to read some kind of a guide about different types of libraries (including concrete solutions), as well as ideas for custom columns, column coloring, adding various data. I actually think it is the one issue that the Calibre manual does not cover, at least not from the point of view I would be interested in.
It could be descriptions of:
- library structures for some common and uncommon library tipes (fiction, textbooks, books for research, articles, magazines, audiobooks) - people use Calibre for all kinds of stuff,
- how to deal with various kinds of data (e.g. how people mark read/no read, genre, edition, other contributors in anthologies, file quality, translations of the same book etc. - one kind of data can be dealt with very differently by various Calibre users; it's not like one method is better than the other and it is generally good to know other people's methods)
- what one can do with tag column, yes/no columns, column coloring etc. - inspirations are always good

.
Good luck with your work!