I have employees who cannot view projects and tasks through the time entry interface, even though they're on the project Resources list and the task Assignee lists. What would be causing this?

Have a look at one of the sub tabs on the specific project page. I think it’s called Preferences. There’s a checkbox that has to be selected to allow time to be recorded to the project. Similarly there’s also one for expenses. (It may be the same one actually)

Those boxes are checked.

Check the role's permission do they have permission to view project(job) record at least. Also it could subsidiary issue if there are multiple subsidiary involved