Perhaps we're not thinking of the same thing. You are talking about the Photo Gallery widget? Yes, it's true that you can't remove that widget from the Android system, but sometimes removing from and then adding back to the home screen fixes problems. Sometimes not.
Okay, I just added this widget to my home screen to check it out. I think I see what you're talking about. When I placed the widget, a pop up window appeared, asking me to choose a specific album, a specific image, or shuffle all images.
If I choose to shuffle all images, I can successfully scroll through all my locally stored images, until I come to a blank one with the spinning circle. I assume this is a Picasa picture (now Google +, I believe) trying to download and fill the square. It never does.
However, if I choose to show a specific album, and choose one that is located on Google + (Picasa), it works fine and scrolls through all the photos in that album. So try that and see how it works for you.
Alternatively, search Google Play Store for apps or widgets that might give you better results. There seem to be quite a few. One is called Picasa Mobile, and another Perfect Tool for Picasa, both with good reviews, though I don't know if they includes widgets. Another is Ultimate Photo Widget, which is a widget only, as the name implies. Anyway, just search for Picasa Web, or Picasa Widget, and you'll see a variety of options.