Thank you for uploading the screenshots.
The 'good' screenshots show the Flash Player version of your gallery.
The 'bad' screenshots show the Mobile Player version (but with a positioning problem, which is why you sometimes see only navigation arrows).
The Mobile Player will be used when Adobe Flash Player is not installed and enabled in the browser (and, unfortunately, even if Adobe Flash Player is installed, browsers are starting to block Flash content by default).
The positioning problem is likely to be due to either:
(1) A bug in SimpleViewer v2.1.3. (Checking the Version History page, certain gallery sizing issues were fixed in SimpleViewer v2.2.0.)
(2) Custom CSS code on your web page conflicting with (and overriding) the Mobile Player's own CSS. Make sure that you do not have any global CSS code on your web page that the gallery might be inheriting.
Juicebox should certainly be a suitable non-Flash alternative.
Please see these two SimpleViewer blog entries for more information on SimpleViewer vs Juicebox.
What does Juicebox Mean for SimpleViewer-Pro Customers?
The End of Flash and What this Means for SimpleViewer.
Juicebox can certainly display PNG files but there are a couple of known problems with JuiceboxBuilder's handling of PNG images. (The developers are aware of these problems and they should hopefully be fixed in a future version.)
When JuiceboxBuilder-Pro resizes PNG files for a gallery, JPEG images are created and any transparency in the PNG files is lost. Transparent regions are rendered as black in the main image but white in the thumbnail.
The solution to this should be to prevent JuiceboxBuilder from processing PNG images by deselecting the 'Resize Images' checkbox on the 'Images' tab.
If this is done, JuiceboxBuilder should just copy the source images across to the gallery's 'images' folder (without any processing). This much is true (images remain untouched) but the PNG images in the 'images' folder are (incorrectly) given '.jpg' file extensions. (The paths in the gallery's 'config.xml' file match and browsers should still be able to display them, though.)
However, thumbnail images are still generated (as JPEG files) and the transparency issue cannot be overcome from within the JuiceboxBuilder interface.
The best course of action when using PNG files with transparency would be to just manually copy them across to the gallery's 'images' folder and then make sure that there is an <image> entry for each PNG image in the gallery's 'config.xml' file. The corresponding imageURL and thumbURL can both point towards a single PNG file. (When the gallery is displayed, Juicebox will dynamically resize the image for use as a thumbnail.)
I hope this helps to explain what you are seeing and how to hopefully work around the problems.
SimpleViewer Support Team