When a document is busy in edit mode, a spinner appears to the right of the document name. If you click on the spinner you get an explanation of what the document is currently doing. In the example below, we can see that it's updating a variable called newCustomer.
Documents will become busy when they are processing requests. Thus, if you click on a page that triggers lots of calculations, and then move onto a new page before the first page has been calculated, and then click on another, and so on, Displayr will get slower and slower until it completes the calculations.
Similarly, if you have two people in a document in Edit mode at the same time, if one user does something resource intensive (e.g., exports all the pages to PowerPoint, which requires every calculation to be updated), the other user will experience slowness.
In View mode, if you have a large number of users and they are doing more computationally expensive actions, such as filtering or using Explore mode, this will use up more resources and, at some point, this will affect users. However, the effect of multiple users in View mode is relatively minor (having 50 or more users interacting at the same time should not be a problem).