I don't even know where to begin. Let's start at the user level since I am also an administrator of this product.
1) Old Clunky UX -- The User Interface and experience is a jump back to the early 90's and Sage has not put any resources into updating it since then. Even if you make your own interfaces for some of the contact screens the system will attempt to wedge them into a frame that never quite fits the way you'd expect it.
2) Searching -- The search functionality of ACT! does not support wildcard searching or fuzzy searching. This means that if you don't know the full spelling exactly of something you'll never find it. Additionally, the search function(s) require that you select what field of the entity (contact, company, task, etc) that you'd like to search. Technically, there is a global search, but it's very slow and still doesn't have wild card functionality.
3) Integrations -- ACT! comes with the "ability" to sync with Outlook (emails, contacts, and calendars), but it rarely works. It may work for a few days and then go out of sync. The built-in calendar will often duplicate items for almost no reason whatsoever. Outlook will also run very poorly when the sync is enabled for tracking of emails and synchronization of calendar/task items.
4) Installations - Now we're getting into the administration of this production. The installation of Act! loves to force users to install SQL Server on their local machines when it isn't required (unless the installation will be functioning as the Act! Server). This is a huge pain when you now need to then uninstall SQL Server from that machine, which would have caused it to slow to a snails pace on a sales person's laptop. Technically, you do need the local instance for performing synchronizations if a user will be off network, but a cloud based solution would be a far better offering. Lastly, in the realm of installations, there is little to no support in performing silent installs or pushing out with group policy.
5) Archaic Administration - Although this is a SQL Server based application it rarely allows you to actually perform maintenance on the database and utilize the scheduled tasks available in the rdbms. Instead you need to use their built-in tools that are kludgy at best with very little insight on what they are actually doing. Additionally, the administration and security features leave a lot more to be desired.
6) Support - The support of this product is terrible. They outsource most of the support to their Partners rather than the company doing any on their own. This leads to working with people that are trained very poorly and there is very little communication between representatives. Very often will you get 3 different answers on how to fix a problem, and none of them will be correct until you call back for the fourth time.
The standard business problem of tracking clients & contacts, sales leads, and managing resources. We have only realized the benefit of this CRM system in giving us an inexpensive centralized place to store this information, but at the most basic level possible.