It is free, so I can hardly complain. Visualisation options are good, and it integrates with a large range of databases. It allows my small organization (a charity) to use Google Sheets as a database (Sheets itself pulling data from Heroku).
Error messages are absolutely unhelpful. Whenever a connection to a data source is lost, a field has been renamed, or other, the error message is always the like of "Error ID:123dsf132".
Google Data Studio team members do not respond to users asking about this serious issue and other issues on the Google Product Forums.
Loading times are slow. It is not possible to refresh just 1 chart on a Dashboard page, so refreshing takes me an entire minute, when I only have 8 charts per Page.
When I took over ownership of the Dashboards from another user, all the charts stopped working (without showing any helpful error message). I had to recreate each data source one by one. I was not shown any way to prove that I did have admin rights over the prior Data sources.
The list of functions with which the user can create statistics is insufficient, much smaller than the Sheets function list. The Help section is very underdeveloped.
Accepted Date and Number formats are only a fraction of common accepted formats, which can make it a headache to "convert" your data formats into formats accepted by Data Studio.
Chart types lack flexibility (ex: with bar charts, I can only have 2 dimensions and 1 statistic).
The UI could be greatly improved. An example : while assembling a new chart, selecting a Data source and Filters is a headache because the names of these items appear truncated in the selectors, which makes a Source/Filter difficult to distinguish from those with similarly starting names.
I have created the company-wide KPI dashboards, spanning acquisition, retention, product engagement, conversion, etc.