I grant you that the user interface for merging Places vs. Merging Place Details can be a little confusing. I have complained about it but it has never been improved.
Here's the tricky part. When you are in the Place List and when you highlight a Place, it shows you any and all Place Details associated with that Place. It looks like you can therefore do things like highlight some Place Details and merge or delete Place Details from where you are. But you can't. Before you can do anything with the Place Details, you first have to click on the Place Details tab. Having done so, you will see a sub-window called Place Details. Only when you get this sub-window can you manipulate the Place Details.
So be really, really sure that you click the Place Details tab and be really, really sure you get a sub-window that says Place Details - not Places. If you get to that point, it should work just fine to Merge or Delete any of the Place Details.
P.S. It's not clear how best to change the Place and Place Details user interface to make it less confusing. The trouble is that you can edit a Place Details by double clicking it and without first clicking on the Place Details tab. But you can't delete or merge Place Details unless you first click on the Place Details tab. It may seem like a difference without a distinction, but I think that's the root cause of the problem. And if you removed the ability to edit a Place Details without first clicking the on the Place Details tab, I'm sure that users would complain about the extra click to edit Place Details (and I'm a prime critic of RM's clickiness). But I think that edit, delete, and merge of Place Details all need to be in the Place Details window instead of edit of Place Details being in the Place window.