I've used Joomla/Mambo for a couple years now and heres a few things that can be a problem depending on the type of site you want:
1) Access levels or ACL in Joomla/Mambo is quite basic. There are a set number of usertypes: visitor, registered user, author, editor, publisher, admin, super admin.
Unfortunately, usergroups is pretty much hard coded. Theres a few hacks out there that extends user groups, and discussion on how to improve the Access Control in Joomla in the Dev team, but there isnt anything showing at the moment that it will improve in the near future.
The worst part about access control is that since there isnt any well defined API, Joomla/Mambo extensions usually just have a simple, logged in or not approach on the website front end, and an Admin or not approach on the backend...
2) The Content Management System built into Joomla/Mambo has only 3 levels: Section, Category, Content Item (article). This can be a problem sometimes but if you plan well, you really only need three levels..
However, Content Management Features is very powerful and amazingly you have fine grain control over display of content.
What controls your content display is actually in the menu parameters. A Joomla Component, can have multiple entries in the menu's, and thus different settings for each menu item.
Example:
You can use the frontpage component to show the latest articles posted on your Joomla/Mambo site by creating a menu item "Home" or similar and setting the menu params to show articles from any section and order by latest articles.
You can also use the same frontpage component to create another menu item called, say... "Technology", and limit the Items shown to the section technology, and order by say, popular articles.
The list goes on, and its not specific to just the frontpage component, its a feature of any component that supports the Joomla/Mambo component parameters API.
This is a very powerful feature that is quite invisible to most users, but developers make sure they build into their applications.
3) Session Management
Joomla/Mambo doesnt have an API for session Managment, and I havent heard of any prompts to even develop one.
One of the main concerns is that this makes it very hard to integrate already existing Open Source Software.
The current session management still has bugs, this may not be a problem if you dont plan to integrate third party software, but if the time came to say install a forum such as Vbulletin with Joomla/Mambo, you run into more headaches that just switching over to Vbulletin...
Take in mind that this is only the problems associated with Joomla/Mambo, the benefits of using the CMS over others is a much longer list