I never had them complain that the stamps weren't valid for postage. As long as it adds up to correct amount they're happy. I do remember reading of a stamp collector who put commemorative stamps on a package only to be told by the clerk that 'collector' stamps weren't valid for postage.
A friend of mine related this story to me a few years ago. Early in 2007 he had purchased a pane of the then new triangular stamps commemorating the 400th anniversary of the settlement of Jamestown. But his initial attempt to use the stamps failed ... his mail item was returned to him undelivered. Attached to the envelope was a note admonishing him to use U.S. postage.
Recently I was in the UK and I wanted to send some postcards. I went to a shop (I was unable to find a post office in the area) and after I bought some postcards I asked if they have stamps. The shopkeeper had a pane of Post & Go stamps, but she told me that they could not be used to send mail to Europe. I left, and later that day I happened to return to the shop when there was another shopkeeper. I asked again, and this time he sold me the stamps, and I sent the postcards.
Edit: Just realized that this thread relates specifically to the USA. Anyway, it shows that such things happen everywhere.
Post offices are an endangered species here. In most areas, we've gone from the substantial Victorian edifices that I remember from my childhood to a corner of a shop whose main business is selling groceries etc. In a newsagent or souvenir shop with a few books of stamps, it will be hit and miss depending on the stock and the know-how of the shop assistant. By contrast, Paris is great for post offices, although you'd no longer get away with their (high) staffing levels in England.