How do I prevent employees entering time and expenses in CORE for incorrect dates, like May 2022 instead of 2023? 

To overcome this problem, you can set the options Time entry should not be saved/deleted if older/newer than in Settings > Time & Expenses > Time Entry. Time entries will not be saved in CORE if the time entry date falls beyond (before or after) the number of days specified here, say 365. These options define the number of days into the past and the future allowed for saving or deleting a time entry. CORE rejects a date more than or less than those number of days. 

This setting works in combination with the Allow adjust date beyond Settings restriction security permission. For instance, if today's date is May 18, 2023, and you enter 365 in both text boxes, CORE will not allow anyone to make time entries older than the year May 18, 2022, and beyond the year May 18, 2024, assuming that you have unchecked the Allow adjust beyond Settings restriction security permission. Similarly, if you want that employees record or edit their time within a week of the current date, you can enter 7, e.g., 7 days before or after the current day.

You can grant selected users permission to enter and edit dates outside this period by adjusting their security settings.