I can't remove a project from my Time Entry screen
If you are on a role with scheduled hours for the current week, then that role/project will show up on the time entry screen automatically. You'll need to go into both of those projects and remove future scheduled/booked hours.
Projects will also remain in the Time Entry screen if it has been pinned (shown as a check mark in the box under the pin icon on the left side of the screen). To remove pinned project uncheck the box and click on the save link at the bottom of the Time Entry screen.
Another reason why a project will remain in your time entry screen is when a project is using detailed task management. With a detailed task plan each task may have a role/resource assigned to it. If you have been assigned to any role the project will appear in your time entry screen regardless of there being no booked hours or being pinned. In this situation you need to be removed from the task in the detailed task plan.
Time entry screen defaults to a week in the past
The user has most likely bookmarked the Projector website for a specific date. An incorrect bookmark url will look something like this:
https://secure.projectorpsa.com/TimeEntry/timeentry.aspx?periodStartDate=04-Oct-2010
Update the bookmark by removing everything after *.aspx.
My time is rejected because 'This role is no longer for this resource'
This is happening because the role was pinned to the time sheet and the role name has been altered since it was pinned there. Unpin the project from the time sheet, search for the project again (by clicking the little icon next to the project name), and re-enter the time. You can then pin the project back to your time sheet at this point and you should not have any problems in the future.