Picasa 3 does not recognize .MTS files correctly and does not handle playback. It does copy the files from flash-ram to hard disc, but does not show them along with the images.
Install the following two
to make it work. Confirmed for me. No longer crashing.
Alternatively http://www.free-codecs.com/download/k_lite_codec_pack.htm will also work.
Found this info at http://productforums.google.com/forum/#!topic/picasa/h9G_WOaldvw