Thanks for the reply Vampidemic. The .m2ts files are downloaded from my Canon HD camcorder Model Vixia HF10. They play flawlessly on the 570 but not on the 670. I don't want to needlessly pay for VideoRedo but maybe I can try the trial version to see if it makes a difference. I just don't understand why LG wouldn't carry forward that part of the software for .m2ts files from the 570 to the 670. But I do agree with you that the manual doesn't list the .m2ts extension.
I'm not that familiar with Handbrake but I basically used the default setting to convert the .m2ts Canon files to .mkv. I'll take another look at the settings.
I know that the early 570 firmware versions had lip sync issues but my final firmware was great for Netflix but not so with the 670.... frustration persits.
One point worth noting is that the unsupported resolution warning occurs with .MP4 files as well as .m2ts and .MP4 is listed in the manual as a supported container. The manual also says that video up to 1920 x 1080 pixels is supported without any limitations being specified for specific containers. This would tell me that the .MP4 "Unsupported Resolution" issue is a bug or undocumented limitation. This may be worth pursuing with LG support. Who knows, maybe if they take note, they might fix the issue with .m2ts files at the same time.
In the meantime, Handbrake probably is not a good application to use for this conversion because it is designed to re-encode the files and make them smaller. By nature, there is a loss in quality inherent in this sort of re-encoding process which likely accounts for the differences you're seeing. Though Handbrake allows a passthrough option for audio, it doesn't seem to do the same for video. What you want to do is to find a way to remux the video and audio from your .m2ts file into a .mkv file without changing the way the video or audio is encoded.
VideoRedo does this and is a great program in general. If you only need to convert files, there are probably much cheaper options. However, one killer feature that VideoRedo offers is frame accurate editing of MPEG2 and H.264 video. There are very few if any other applications that offer this feature, so if you anticipate the need to edit your home videos without quality loss, this app is worth consideration for that functionality among other things.
If you're looking for free options to do a conversion, it might be necessary to find one tool to "demux" your .m2ts into separate audio and video streams, then use another tool to remux the files. This thread discusses some options:
Unfortunately, the free options do not seem very straight forward for doing this type of conversion. It seems that most people would just assume have smaller files and are not all that concerned with preserving the quality of their videos.
It may be possible to use a DLNA server to do this conversion on the fly, though depending on the bit rate of your files and the speed of your network, this might not be feasible. I have had trouble playing MPEG2 1080i content captured from my cable box over my wireless N network (without even doing any conversion); it's not quite fast enough to keep up with the bit rate of the files, so the videos studder a lot. This may or may not be an issue over a faster wired network.