The best point to solicit a contribution is when a user is looking at the data. A data user might have identified a problem and fixing it will help them continue with their current task. A contributor may be interested in a specific record or have some knowledge or expertise to share that could improve the data.
Providing a clear prompt for users to edit a record, fix an error in a field, or add a missing value as a Suggested Edit, will help them understand that they can contribute to the project.
If a user isn’t able to edit a record or field, then using Error Reporting will allow them to flag quality issues when they encounter them.