I took the example from the docs and added another feature. On clicking the feature data will be displayed in a popup. I add another feature with different data. If I click the features in series it'll show the data from the first feature I clicked. If I click a feature, click somewhere else and then the other feature: It works like expected.
I've created a jsfiddle showing this problem. (In my firefox the map will only show if I click on the 'shield' icon in the top-left corner of the address bar and select 'Disable Protection on This Page'. See this question)
Seems like the correct feature is not taken using this example code:
// display popup on click
map.on('click', function(evt) {
  var feature = map.forEachFeatureAtPixel(evt.pixel,
      function(feature, layer) {
        return feature;
      });
  if (feature) {
    var geometry = feature.getGeometry();
    var coord = geometry.getCoordinates();
    popup.setPosition(coord);
    $(element).popover({
      'placement': 'top',
      'html': true,
      'content': feature.get('name')
    });
    $(element).popover('show');
  } else {
    $(element).popover('destroy');
  }
});
My goal is to click on the features directly one by one and get the correct data displayed.
EDIT: Seems like it's not a problem of OpenLayers but of the popover. When I insert:
console.log(feature.get('name'));
It'll come up with the correct data.
 
    