It seems that inline editing is not available on promotions. Is there a list somewhere of records that do not support inline editing? Or, could I be doing something wrong? I have tried the default promotions view, customizing the default view, and using a new saved search. I made sure that the searches do not use expressions on the Criteria tab. Anything else?

There's definitely a lot of limitations on inline editing. For me it's often a surprise whether or not it will work on a Saved Search result. A quick Google produced these known limitations -- none that specifically deal with promotions, but it's possible the promotions record type is just not supported, too. • Record status: Inline editing doesn't work for records that are inactive. • List view filters: Inline editing only works for lists with a single record type filter. It doesn't work for list views with six or more filters. • Lookup filter criteria: Fields used in lookup filter criteria can't be modified with inline editing. • Long text and rich text area fields: These fields can't be edited with inline editing. • Referenced fields: If a field on a record is referenced by a formula custom field, it can't be edited with inline editing. • Sublists and subrecords: SubmitFields can't be used to modify fields in a sublist or subrecord. • User role: Inline editing may not work if the user's role has the "Restrict Time and Expenses" preference enabled, or if the user's role doesn't have the "Find Transaction" permission. • Transaction list or saved search: Inline editing may not work if the user tries to use it on a transaction list or saved search that has multiple transaction types