Nothing in the log, but stdout shows some GL errors like "Impossible to create render texture (failed to link the target texture to the frame buffer)". Someone mentioned a similar problem in this thread:
http://forum.attractmode.org/index.php?topic=1878.0
I tried increasing the GPU memory from 256 to 512 (the Pi 3 has 1 gig of RAM to split between CPU/GPU), but that didn't help. I guess the Pi just isn't strong enough for the fancier themes.
The Pi 3 can use layouts/themes that use the carrier.nut. Oomek's Silky layout is an example that works well on the Pi. The white boxes you describe do sound like they can be a memory issue or missing/misconfigured artwork (some layouts use different folder names for the artwork assets).
If you are running RetroPie make certain that you're booting to a command line or directly to Attract-Mode. Booting to Emulation Station or Pixel Desktop first and then running Attract-Mode will consume more GPU memory and possibly cause issues. 256MB - 384MB is good setting for your Pi GPU.
Some layouts/themes are created by people using Windows which is NOT case sensitive. These layouts can have problems when they are run on Linux (which is case sensitive) if the author hasn't taken this into account.
I haven't really come across any layouts that won't work on the Pi and I've tried just about everything over the years. They all work but some are so GPU and/or CPU heavy that they will run very slow (to the point you wouldn't want to use them). Make sure that you look at the layout settings if a layout runs slow or doesn't look right. Most layouts have features that can be adjusted/disabled which can speed things up or correct artwork folder issues.
Last thoughts, make sure you're using hardware video decoding (mmal) and not software decoding. Also make sure that your videos aren't too high resolution.
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