Thanks for trying the beta Josef and spotting this - the main developers both use PostgreSQL, so this would have slipped out in the release probably if you hadn't brought it to our attention!
All but one of the fields in UniqueEquipmentNames are text fields, and from what I have read based on your message below is that MySQL can't guarantee uniqueness on fields that are potentially longer than 255 characters.
I've created an issue for this on bitbucket - it might be best to track progress from there. I've proposed two possible solutions there, and I want to get David Platten's opinion on it before we create a solution.
Kind regards, and thanks again.
Ed